The purpose of this article is to present a user friendly and reasonably detailed exposition of ideas and tools of equivariant Topology which have proven to be useful in Combinatorics. This paper can also be viewed as a continuation of the chapter ``Topological methods'' prepared for the CRC Handbook of Combinatorics [57]. Our intention is to develop an overall picture emphasizing a typical scheme of applications. Some technical details, which are often skipped in existing expositions, are isolated and discussed. On the technical side we emphasize the role of the so called cohomological index theory. We hope that the clarification and systematization of ideas will encourage a nonexpert to use freely these tools in his or her own research. (Introduction)