The past decades have seen a substantial change in the importance of private (PI) relative to social insurance (SI), to the advantage of the latter. The efficiency view of SI (to be expounded in Sect. 2) explains the existence of SI with the market failures of PI, namely, moral hazard and adverse selection. In Sect. 3, a benevolent government is introduced that seeks to determine the optimal division of labor between PI and SI. However, moral hazard effects are found to plague SI at least as much as PI, while the empirical relevance of the adverse selection argument has recently been challenged. In Sect. 4, the exposition therefore turns to the public choice view, which emphasizes the interests of risk-averse voters even with above-average wealth in redistribution through SI. This view predicts a crowding-out of PI by SI also in markets without adverse selection, which has been observed. Section 5 turns to normative issues by proposing a test that indicates whether and in which lines of insurance the division of labor between PI and SI could be improved. The final Sect. 6 offers concluding remarks and an outlook on future challenges confronting both PI and SI.