This chapter describes about the challenges which cannot be handled by simply improving markets and making them competitive or by turning them over to the government. The term externality has been coined to remind us that the cost occurs without the intermediation of markets; that is, it is external to the system of markets. The root of the externality problem is that either producers or buyers get something without the mediation of markets. Market failure, however, is not always the result of a missing market. There are some peculiar goods and services that induce market failure by their very nature. Under-revelation of preference for public goods is a widespread phenomenon. Quite appropriately it is called 'free-riding'. Markets with information asymmetry cannot function as efficient markets. Education and health care have some special issues. If education is provided only by private institutions, it will be produced to satisfy its market demand.