This contribution seeks to answer two related questions. First, what is the purpose of social health insurance? Or put in slightly different terms, what are the reasons for social (or public) health insurance to exist, even to dominate private health insurance in most developed countries? And second, what are the limits of social health insurance? Can one say that there is too much social health insurance in the following two senses: Should the balance be shifted towards the private alternative? And is the degree of coverage excessive? Accordingly, the plan of this paper is as follows. Section 2 is devoted to the efficiency, public choice, and equity reasons that may explain the existence (but not necessarily the prominence) of social health insurance. After having examined the demand for social insurance, its supply is analyzed in section 3. A simple model expounding the trade-off between innovation and risk selection effort of a private and a social health insurer will be developed. The innovation dimension importantly comprises efforts at containing moral hazard; therefore, the model may provide a preliminary answer also to the issues of 'excessive coverage provided by social health insurance'. This is followed by the economic theory of the optimal health insurance contract in section 4, which provides the benchmark for a discussion of actual outcomes of both a private and a regulated social health insurance market (section 5). It would be preferable to be able to describe and evaluate 'equilibria'; however, there is not only a price and a single quality dimension to be determined and evaluated. Therefore, the discussion will be somewhat descriptive at this points. Section 6 provides a survey of the future challenges confronting health insurance and an assessment of social and private insurance to cope with them. The final section offers a few conclusions and suggestions for future research.