Due to their cost, performance, area, and energy efficiency, MPSoCs offer appealing architecture for emerging mixed criticality systems (MCS) such as driverless cars, smart power grids, and healthcare devices. Furthermore, heterogeneity of MPSoCs presents exceptional opportunities to satisfy the conflicting requirements of MCS. Seizing these opportunities is unattainable without addressing the associated challenges. We focus on four aspects of MCS that we believe are of most importance upon adopting MPSoCs: theoretical model, interference, data sharing, and security. We outline existing solutions, highlight the necessary considerations for MPSoCs including both opportunities they create and research directions yet to be explored.