The l-adic étale cohomology of a variety is defined in terms of the geometry of l-power degree coverings. Unlike in algebraic topology, there is no integer-valued theory to compare with, leading to a plethora of "independence of l" conjectures for varieties over finite fields. We will survey what is known, and prove that independence of l for Betti numbers is equivalent to independence of l for homological equivalence of algebraic cycles.