Tapenade is an Automatic Differentiation tool which, given a Fortran or C code that computes a function, creates a new code that computes its tangent or adjoint derivatives. Tapenade puts particular emphasis on adjoint differentiation, which computes gradients at a remarkably low cost. This paper describes the principles of Tapenade, a subset of the general principles of AD. We motivate and illustrate on examples the AD model of Tapenade, i.e. the structure of differentiated codes and the strategies used to make them more efficient. Along with this informal description, we formally specify this model by means of Data-Flow Equations and rules of Operational Semantics, making this the reference specification of the tangent and adjoint modes of Tapenade. One benefit we expect from this formal specification is the capacity to study formally the AD model itself, especially for the adjoint mode and its sophisticated strategies. This paper also describes the architectural choices of the implementation of Tapenade. We describe the current performances of Tapenade on a set of codes that include industrial-size applications. We present the extensions of the tool that are planned in a foreseeable future, deriving from our ongoing research on AD.