Numerous feature-based models have been recently proposed by the information retrieval community. The capability of features to express different relevance facets (query- or document-dependent) can explain such a success story. Such models are most of the time supervised, thus requiring a learning phase. To leverage the advantages of feature-based representations of documents, we propose TournaRank, an unsupervised approach inspired by real-life game and sport competition principles. Documents compete against each other in tournaments using features as evidences of relevance. Tournaments are modeled as a sequence of matches, which involve pairs of documents playing in turn their features. Once a tournament is ended, documents are ranked according to their number of won matches during the tournament. This principle is generic since it can be applied to any collection type. It also provides great flexibility since different alternatives can be considered by changing the tournament type, the match rules, the feature set, or the strategies adopted by documents during matches. TournaRank was experimented on several collections to evaluate our model in different contexts and to compare it with related approaches such as Learning To Rank and fusion ones: the TREC Robust2004 collection for homogeneous documents, the TREC Web2014 (ClueWeb12) collection for heterogeneous web documents, and the LETOR3.0 collection for comparison with supervised feature-based models.