The Tate conjecture and semisimplicity of Galois representation

Consider smooth projective varieties over finitely generated fields of characteristic 0. The Tate Conjecture is often stated as having two parts: one assertion (S) about semisimplicity of Galois representations on the cohomology, and an assertion (T) saying that all Tate classes are algebraic. In my talk I will explain that in fact (T) implies (S). This uses some basic properties about motives. My talk is aimed at non-experts, and I will spend a large part of it on an introduction to the underlying ideas.