Hundreds of millions of users each day search the web and other repositories to meet their information needs. However, queries can fail to find documents due to a mismatch in terminology. Query expansion seeks to address this problem by automatically adding terms from highly ranked documents to the query. While query expansion has been shown to be effective at improving query performance, the gain in effectiveness comes at a cost: expansion is slow and resource-intensive. Current techniques for query expansion use fixed values for key parameters, determined by tuning on test collections. We show that these parameters may not be generally applicable, and, more significantly, that the assumption that the same parameter settings can be used for all queries is invalid. Using detailed experiments, we demonstrate that new methods for choosing parameters must be found. In conventional approaches to query expansion, the additional terms are selected from highly ranked documents returned from an initial retrieval run. We demonstrate a new method of obtaining expansion terms, based on past user queries that are associated with documents in the collection. The most effective query expansion methods rely on costly retrieval and processing of feedback documents. We explore alternative methods for reducing query-evaluation costs, and propose a new method based on keeping a brief summary of each document in memory. This method allows query expansion to proceed three times faster than previously, while approximating the effectiveness of standard expansion. We investigate the use of document expansion, in which documents are augmented with related terms extracted from the corpus during indexing, as an alternative to query expansion. The overheads at query time are small. We propose and explore a range of corpus-based document expansion techniques and compare them to corpus-based query expansion on TREC data. These experiments show that document expansion delivers at best limited benefits, while query expansion, including standard techniques and efficient approaches described in recent work, usually delivers good gains. We conclude that document expansion is unpromising, but it is likely that the efficiency of query expansion can be further improved.