This talk will describe algorithms developed for the statistical analysis of contingency tables. Classical methods for statistical analysis such as the chi-squared test of independence rely on large sample approximations. When tables contain many cells with low counts these approximations can be very inaccurate leading to erroneous conclusions. We will discuss computationally intensive methods that are exact and use network representations of the problem. Algorithms based on a network view today represent the state of the art in terms of computational efficiency for many commonly used contingency table tests.