We introduce the topical relevance model (TRLM) as a generalisation of the standard relevance model (RLM). The TRLM alleviates the limitations of the RLM by exploiting the multi-topical structure of pseudo-relevant documents. In TRLM, intra-topical document and query term co-occurrences are favoured, whereas the inter-topical ones are down-weighted. The multi-topical nature of pseudo-relevant documents results from the multi-faceted nature of the information need typically expressed in a query. The TRLM provides a framework to estimate a set of underlying hypothetical relevance models for each such aspect of the information need. Experimental results show that the TRLM significantly outperforms the RLM for ad-hoc and patent prior art search, and additionally that it outperforms recent extensions of the RLM.