The fixed-parameter approach is an algorithm design technique for solving combinatorially hard (mostly NP-hard) problems. For some of these problems, it can lead to algorithms that are both efficient and yet at the same time guaranteed to find optimal solutions. Focusing on their application to solving NP-hard problems in practice, we survey three main techniques to develop fixed-parameter algorithms, namely: kernelization (data reduction with provable performance guarantee), depth-bounded search trees and a new technique called iterative compression. Our discussion is circumstantiated by several concrete case studies and provides pointers to various current challenges in the field.