Dealing with the complexity of the human biosystem in drug discovery is a daunting task. At best we have an imperfect picture of its underlying physiology and pharmacology, which raises the question of how to identify potential drug compounds from the vast sea of xenobiotics that populate chemical space. The dominant approach is still based on the single-Target paradigm, which has a number of inherent problems not the least of which is the difficulty of altering disease phenotypes by intervening at single targets embedded within complex, interconnected biological pathways. While newer multi-Target approaches address some of the problems, they are not entirely without problems of their own. Superimposed on all of these difficulties is a surprising lack of compound and target specificity that the growing amount of data clearly shows is a more pervasive problem than has generally been assumed. And although sophisticated phenotypic screening methods are being developed in an effort to deal with some of these issues, many remain refractory.