Evolutionary algorithms and other nature-inspired search heuristics like ant colony optimization have been shown to be very successful when dealing with real-world applications or problems from combinatorial optimization. In recent years, analyses has shown that these general randomized search heuristics can be analyzed like "ordinary" randomized algorithms and that such analyses of the expected optimization time yield deeper insights in the functioning of evolutionary algorithms in the context of approximation and optimization. This is an important research area where a lot of interesting questions are still open.The tutorial enables attendees to analyze the computational complexity of evolutionary algorithms and other search heuristics in a rigorous way. An overview of the tools and methods developed within the last 15 years is given and practical examples of the application of these analytical methods are presented.