Ergodicity, which says that the orbit of almost every point explores all regions of the state space, is a form of mixing. In Bernoulli shifts, where the probability that \(x_n=i\) is independent of history, one has another form of mixing. In this chapter, we will discuss a number of properties representing various degrees of mixing between ergodicity and independence. Their relations can be summarized as \(\{\) ergodic \(\} \ \supset \{\) weak mixing \(\} \ \supset \ \{\) mixing \(\} \ \supset \{\) exact/K \(\} \ \supset \ \{\) Bernoulli \(\}\) , meaning ergodicity is the weakest and Bernoulliness the strongest.