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The aim of this paper is to survey some known results about mapping classgroup quotients by powers of Dehn twists, related to their finite dimensionalrepresentations and to state some open questions. One can construct finitequotients of them, out of representations with Zariski dense images intosemisimple Lie groups. We show that, in genus 2, the Fibonacci TQFTrepresentation is actually a specialization of the Jones representation.Eventually, we explain a method of Long and Moody which provides large familiesof mapping class group representations.

On mapping class group quotients by powers of Dehn twists and their representations