Searching for departures from statistical independence in data is a fundamental problem that has been formalized in a variety of ways. We will cover two frameworks in which this problem has historically been understood. The first is statistical and involves framing the search as a hypothesis test in a finite-sample setting. The second is probabilistic and involves defining functions of random variables that have useful properties in the large-sample limit. We will close with a discussion of common themes underlying measures of dependence arising from each of these paradigms.