The so-called market model has been the benchmark model for pricing interest-rate derivatives since 1997. However, the market model has a serious limitation: it cannot generate any non-flat implied volatility curve, which is a very persistent presence with major interest-rate derivatives. In this presentation, we will first offer a brief introduction of the market model, then we will describe various extensions intended to model observed implied volatility curves. Particular attention will be given to market model with stochastic volatility. Outstanding challenges in analysis and implementation will be discussed.