Market liquidity is the ease of trading an asset. Its risk is the potential loss, because a security can only be traded at high or prohibitive costs. While the omnipresence and importance of market liquidity is widely acknowledged, it has long remained a more or less elusive concept. Treatment of liquidity risk is still under development. This paper provides an overview on important aspects of market liquidity and its risk. We also survey existing models to integrate market liquidity risk into risk frameworks. We place special emphasis on practical usability and discuss relevant strengths, weaknesses and their implications.