In my first talk I will recall the historical motivation for the introduction of log geometry, and review the basics of the theory : the language of log schemes, charts, differentials, log smoothness and log regularity. In the second one, I will briefly discuss two applications, whose statements involve no log geometry but whose proofs use it as an essential tool : (a) Gabber's refined de Jong's theorems (b) p-adic - de Rham comparison theorem (new proof by Beilinson).