It has been understood since the late 1960s that tools and structures arising in mathematical logic and proof theory can usefully be applied to the design of high level programming languages, and to the development of reasoning principles for such languages. Yet low level languages, such as machine code, and the compilation of high level languages into a low level ones have traditionally been seen as having little or no essential connection to logic. However, a fundamental discovery of this past decade has been that low level languages are also governed by logical principles. From this key observation has emerged an active and fascinating new research area at the frontier of logic and computer science. The practically-motivated design of logics reflecting the structure of low level languages (such as heaps, registers and code pointers) and low level properties of programs (such as resource usage) goes hand in hand with the some of the most advanced contemporary researches in semantics and proof theory, including classical realizability and forcing, double orthogonality, parametricity, linear logic, game semantics, uniformity, categorical semantics, explicit substitutions, abstract machines, implicit complexity and sublinear programming.