I will give an overview of the most important results about stationary random walks on  SL(k, R). We will talk about Lyapunov exponent and their properties, such as positivity of the top exponent, simplicity and regularity of the spectrum and others. We will also mention other limit theorems, such as central limit theorem and law of iterated logarithm. The talk is based on the monograph ``Random walks on groups and random transformations'' by Alex Furman.