The first mortgage backed security (MBS) was issued in 1968. Thereafter, the MBS market grew rapidly with outstanding issuance's exceeding $9 trillion by 2010. The growth in the MBS market was accompanied by numerous innovations such as the collateralized mortgage obligations (CMOs) and the emergence of private label alternatives to MBS issued by government sponsored entities. We trace the evolution of the MBS market and we review debates surrounding such questions as whether the MBS market has reduced the cost of housing finance, whether the MBS market is a market for lemons, and what role, if any, MBS played in the run-up and subsequent decline of home prices during the decade of the 2000s. We also detail the evolution of models for MBS valuation as developed by academics and practitioners.