Abstract: In these expository talks, I will describe some results by Carlos Bocker-Neto and Marcelo Viana showing that locally constant GL(2,C)-cocycles over Bernoulli shifts depend continuously on the cocycle and on the invariant probability. In the first talk I will present the relevant definitions, background and main theorems. In the second part I will present a step in the proof that reduces the problem to that of a diagonizable cocycle. References: 1. Continuity of Lyapunov exponents for random 2D matrices, Carlos Bocker-Neto and Marcelo Viana 2. Lectures on Lyapunov exponents, Marcelo Viana