A set of 2 by 2 matrices with determinant 1 is called "hyperbolic" if the norms of all products of matrices in the set grow uniformly exponentially fast with product length. A good way to study this notion is to regard each matrix as a map on projective space, and to consider the associated "iterated function system" (IFS). I will present a simple characterization of hyperbolicity in terms of the IFS dynamics. I will also explain the natural generalization of the hyperbolicity concept for higher dimension. Back in dimension 2, there are several interesting questions, most of them open, about the set of hyperbolic n-tuples. This "hyperbolicity locus" is completely understood for n=2, but gets much more complicated for n=3. If time allows, I will discuss the relations of some of these problems with deformation of Riemann surfaces. This talk is based on joint work with A. Avila, N. Gourmelon, and J.-C. Yoccoz.