This book covers the almost eighty years from Turing's seminal paper of 1936 to the present and focuses on two developments during that period. On the one hand, the development of computability theory and complexity theory called for generalizations, restrictions, and other modifications of Turing's original machine. On the other hand, it became clear that recursion theory cannot serve as a foundational analysis of the notion of computable function(al), which has to be accepted as primitive. In different ways, both of these developments contributed to a unified view of logic.