The independent set problem is that of finding a maximum size set of mutually non-adjacent vertices in a graph. The study of independent sets, and their alter egos, cliques, has had a central place in combinatorial theory. The current paper is not meant to be the ultimate summary of independent set approximation algorithms, but an introduction to the performance ratios known, the strategies that have been applied, and offer glimpses of some of the results that have been proven. We prefer to study a range of algorithms, rather than seek only the best possible performance guarantee. The latter is fine as far as it goes, but is not the only thing that matters; only so much information is represented by a single number. Algorithmic strategies vary in their time requirements, temporal access to data, parallelizability, simplicity and numerous other factors that are far fromirrelevant. Different algorithms may also be incomparable on different classes of graphs, e.g. depending on the size of the optimal solution. Finally, the proof techniques are perhaps the most valuable product of the analysis of heuristics.