This text reviews material from more than 300 publications on the oscillation theory of difference and functional differential equations of various types. For difference equations, a large number of new concepts is explained and supported by theoretical developments. For differential equations, simplified versions of several new integral criteria for oscillations are presented. Proofs which illustrate the various strategies and ideas involved are given. This book should be a stimulus to the further development of the theory. It should be of interest to mathematicians and graduate students in the disciplines of theoretical and applied mathematics.