Given a projective variety X, the k-secant variety \sigma_k(X) is the union of the linear span of any k points in X. So the 2-secant variety is the usual secant variety. This is a classical subject, that has recently received further motivations from its applications to signal processing and to other areas. In this introductory talk, I will describe classical results and focus on some open problems. I will touch upon the polynomial. Waring problem, the rank of a tensor (including the Comon conjecture) and a nice example regarding plane quartics. A good introduction is Ciliberto's talk at ECM 2000