Vectors, matrices and tensors are the mathematical objects universally used to describe scientific phenomena, engineering processes, and numerical algorithms. By contrast, processors only operate with scalars and small arrays, and do not understand the language and the rules of linear algebra. Because of this mismatch, any linear algebra expression has to be translated in terms of the instructions supported by the specific target processor. Over the course of many years, the linear algebra community has put tremendous effort in the identification, standardization, and optimization of a rich set of relatively simple computational kernels--such as those included in the BLAS and LAPACK libraries--that provide the necessary building blocks for just about any linear algebra computation. The initial--daunting--task has thus been reduced to the decomposition of a target linear algebra expression in terms of said building blocks; we refer to this task as the "Linear Algebra Mapping Problem" (LAMP). However, LAMP is itself an especially challenging problem, requiring knowledge in high-performance computing, compilers, and numerical linear algebra. In this talk we present the problem, we give an overview of the solutions provided by several programming languages and computing environments (such as Julia, Matlab, R, ...), and introduce Linnea, a compiler to solve the general form of LAMP. As shown through a set of test cases, Linnea's results are comparable with those obtained by a human expert.