Abstract : « In a series of groundbreaking papers published about fifty years ago, Alan Baker developed the theory of linear forms in logarithms of algebraic numbers. He proved that any expression of the form $$beta_0 + beta_1 log alpha_1 + cdots + beta_n log alpha_n, $$where $alpha_1, ldots , alpha_n, beta_1, ldots , beta_n$ are non-zero algebraic numbers and $beta_0$ is algebraic, vanishes only in trivial cases. He was also able to bound from below its absolute value (when non-zero). Such estimates have numerous applications in Diophantine approximation, in the theory of Diophantine equations, and also in various other domains. We discuss some of them.