In this thesis, we discuss a family of sampling methods known as Markov chain Monte Carlo (MCMC) algorithms. To support the analysis of such algorithms,we developed the software tool marathon, designed to determine properties of Markov chains that are usually hard to find analytically. We apply our software to experimentally assess the efficiency of several MCMC algorithms from three sampling applications. First, we address three well-known MCMC algorithms for the uniform sampling of bipartite graphs with fixed degrees. In a set of experiments, we show which sampling algorithm works best in certain types of ecological applications. Motivated by the work with incomplete data, we next address the uniform sampling of bipartite graphs whose degrees lie in prescribed intervals. After introducing two new MCMC algorithms, we give a proof of their correctness and experimentally assess their efficiency. Finally, we address the uniform sampling of perfect matchings in bipartite graphs. In a set of experiments with two special classes of bipartite graphs, we identify initial states that require a polynomial and an exponential number of steps.