We have explored methods for music information retrieval for polyphonic music stored in the MIDI format. These methods use a query, expressed as a series of notes that are intended to represent a melody or theme, to identify similar pieces. Our work has shown that a three-phase architecture is appropriate for this task, in which the first phase is melody extraction, the second is standardisation, and the third is query-to-melody matching. We have investigated and systematically compared algorithms for each of these phases. To ensure that our results are robust, we have applied methodologies that are derived from text information retrieval: we developed test collections and compared different ways of acquiring test queries and relevance judgements. In this paper we review this program of work, compare to other approaches to music information retrieval, and identify outstanding issues.