For the past four centuries, the attempt to answer this question has been the main driving force of world history not only the history of ideas, but also the history of politics and collective violence. This is true for two reasons:
1. It is impossible for people to live without constructing some cognitive structure (which philosophers call practical reason) that asks and answers questions concerning how to live and what to do traditionally, by formulating them in moral or ethical terms as how we should live and what we ought to do.
2. When humanity made the transition, at the time of the scientific revolution of the 17th century, to a new and higher stage of its collective cognitive development by progressing from theology and philosophy to science, it became more and more difficult for people to see how it could be possible to answer the old pre scientific theological and philosophical questions, "what is good and what is evil?" Those questions came to be seen as unanswerable and hence meaningless because what the scientific revolution showed, above all, was that what we call "knowledge" (scientia) is possible when, and only when, it can be framed in the form of hypotheses that can be confirmed or disconfirmed by means of experience, i.e., empirical data and observations.
That entailed, for example, the conclusion that metaphysical knowledge (knowledge of Absolute Reality, or God, as It, He or She exists independently of our perceptual and conceptual apparatus) is unattainable. (Nietzsche called this the "death of God.") But that was not an insuperable problem, because metaphysics was immediately replaced by physics, which had far greater cognitive power to predict, explain and control the phenomena being cognized anyway.
What has been an insuperable problem, up to now, has been the unavailability of any cognitively adequate replacement for ethics. Moral knowledge is unattainable because there is, in principle and by definition, no conceivable moral hypothesis that could possibly be proved or disproved by means of any conceivable type of empirical data, test or experiment. That is true, among other reasons, because moral statements do not take the form of empirically testable hypotheses, or hypothetical imperatives ("If you want X, then you can get it by doing Y" - but with no guidance as to whether you should want X in the first place). Moral statements take the form of value judgments and categorical imperatives (i.e., commandments or orders as to what you should do or want). Commandments can never be true or false, so they cannot communicate knowledge. And value judgments are incapable of communicating knowledge about the external world; the only thing they can express are subjective wishes, tastes and preferences which are, from a logical and epistemological point of view, completely non-rational and arbitrary, matters of whim, about which we can only say De gustibus non disputandum est.
Of course, it has always been known that beauty exists in the eye of the beholder. What had not been seen so clearly, until the scientific revolution, was that the same was true of good and evil. The first modern personality, Hamlet, expressed this clearly in 1601 when he said "There is nothing either good or bad but thinking makes it so." I.e., good and evil are words for subjective preferences, sentiments of approval or disapproval, that exist only in the mind of the beholder. They do not exist as objective realities whose validity can be known or tested, proved or disproved. And Hamlet's fate shows how confused, paralyzed, violent and self-destructive people can become when they have recognized that it is impossible to know what one "should" do, but have not yet discovered how to replace that question with one that is answerable.
Thus, it is not only God (and the Devil) that are dead; more importantly, so are Good and Evil, the abstract philosophical concepts of which the former are the concrete mythological and theological incarnations. As Ivan Karamazov put it (speaking for those for whom God is the only credible and legitimate source of moral authority), "without God anything is possible, everything is permitted." But even those who, following Kant or Rawls, would like to place their faith in pure (a priori) reason, and would trust it to take the place of God as the source of moral knowledge, are doomed to disappointment and ignorance; for even Kant made it clear that moral knowledge was unattainable. As he put it, "I must destroy knowledge in order to make room for faith (Glaube, also translatable as "belief")." That is, even the most dedicated champion of pure (a priori) practical reason as the source of moral knowledge had to admit that moral knowledge is unattainable; all he could put in its place was faith. And by the time he wrote those words, the Age of Faith had long since been dead and buried. Indeed, the whole history of modern science was one long demonstration that knowledge was attainable when, and only when, one replaced faith with its opposite, the attitude of universal doubt, and refused to believe any proposition that had not been tested against empirical evidence.
One inescapable consequence that followed from all this was the loss of credibility of the traditional sources of moral authority (God and pure reason). Why did that create such a crisis that most of human history since the 17th century has been a series of attempts to come to terms with it, both in theory and in practice? Because human nature abhors a cognitive vacuum, especially in the sphere of practical reason. For without some way of answering the questions that practical reason asks, concerning how to live and what to do, humans are totally disoriented and without direction, a condition that is intolerable and panic-inducing. Once they have discovered the cognitive inadequacies of the moral way of formulating those questions and answers, as they have to an increasing extent since the scientific revolution of the 17th century, and have not yet discovered how to progress to a more cognitively adequate form of practical reason, many people will regress to a more intellectually primitive and politically reactionary set of questions and answers. In the 20th century these took the form of political totalitarianism, which led to genocide; more recently, they have taken the form of religious fundamentalism, which has increasingly led to apocalyptic terrorism. Given the existence of weapons of mass destruction, it hardly needs to be stressed how much both of these ideologies potentially threaten the survival of our species.
These political/ideological movements have been widely, and correctly, interpreted as rebellions or reactions against modernity (whether modernity is conceived of as Western civilization, Jewish science, modern technology, religious unbelief, freedom to express any opinion, or whatever), though usually without specifying what it is about modernity that threatens our very existence and survival. The deepest threat, I would maintain, is cognitive chaos in the realm of practical reason, and thus nihilism in the realm of morality, anomie in the realm of law, and anarchy in the realm of politics. The paradox is that the political movements that have been most widely interpreted as nihilistic and "evil" - Nazi, Stalinist and theocratic totalitarianism and their sequelae, genocide and terrorism in fact originated as desperate (and misguided) attempts to ward off nihilism and what their adherents consider "evil." To them, the greatest evil is modernity, on in other words, the modern scientific mentality, which replaces certainty with doubt, dogmatism with skepticism, authority with evidence, faith with agnosticism, coercion with persuasion, violence with words and ideas, and hierarchy with democracy and equality of opportunity all of which fills them with overwhelming dread and terror, amounting to a kind of existential or moral panic.
In fact, to the totalitarian/fundamentalist mind, modernity not only represents absolute evil; it represents something even worse than that, namely, the total absence and delegitimation of any standards of good and evil whatsoever the total death of good and evil, a state of complete anomie and nihilism. For without knowing what is good and evil, how can one know what to do? And without knowing what to do, how can one live (not only biologically, but even mentally)? How can one maintain any mental, emotional, social, cultural or political coherence and order? As Kenneth Tynan remarked, "Hell is not the place of evil; rather, Hell is the absence of any standards at all." That condition is so intolerable to humans that many will regress to even the most irrational and destructive ideology if they cannot find some more epistemologically powerful cognitive structure with which to replace the old moral way of thinking, once its cognitive inadequacy has been so deeply perceived that its credibility has been irreversibly destroyed.
Cognitive growth occurs by finding better and better answers to existing questions. Cognitive development occurs only when one begins to ask a new and different set of questions. We do this only when we notice that our current questions are meaningless because they are unanswerable, so that they need to be replaced with a different set of questions that can be answered. By this point, in the 21st century, we now realize that it is impossible to answer the moral (and legal and political) questions, "How should we live and what ought we to do?" The only questions that are meaningful, in that they can lead to answers that possess cognitive content or knowledge, are the questions "How can we live? i.e., what biological, psychological and social forces, processes and behavior patterns promote, protect and preserve life, and which ones cause death?" For that question can be answered, by means of empirical investigation as to the causes and prevention of the extinction of species (including our own, as by nuclear holocaust or unrestrained devastation of our natural environment), the extermination of social groups (through epidemics of collective violence, such as war, genocide, poverty, famine, etc.), and the deaths of individuals (by means of homicide, suicide, obesity, alcoholism, etc.). In other words, the only possible replacement for ethics or morality that is progressive rather than regressive is the human sciences human biology, psychology and psychiatry, and the social sciences.
Unfortunately, the modern human sciences, unlike the natural sciences, had not yet been invented when the scientific revolution of the 17th century first showed that moral knowledge was unattainable. And even today, the ability of the human sciences to predict, explain and control the objects of their scrutiny (human behavior) is extremely limited, whether compared with that which the natural sciences possess with respect to their objects of study, or with the degree of cognitive power that the human sciences will need to attain if we are to gain the ability to avert the headlong rush to species-wide self-destruction that we currently seem to be embarked upon. In other words, to paraphrase Winston Churchill's remark about democracy, the human sciences are the worst (the least cognitively adequate) of all possible forms of practical reason except for all the others (such as moralism, fundamentalism and totalitarianism)! What that implies is that nothing is more important for the continued survival of the human species than a stupendously increased effort to make progress in the further development of the human sciences, so as to increase our understanding of the causes of the whole range of our own behaviors, from life-threatening (violent) to life-enhancing.