The purpose of this paper is to give an overview of the roles, objectives, and trade-offs in a two-pillar pension system consisting of tax-financed, public pensions and defined contribution, individual pensions. A pension system has many moving parts and our aim is to provide the reader with an understanding of how the parts interact and work together, a theme rarely addressed in the literature. In the first part of this paper, we give a qualitative overview of market failures, behavioural aspects, and distributional issues that form the background for a multi-pillar pension system design with mandatory components. In the second part of this paper, we present three thematic, quantitative analyses that illustrate fundamental relationship concerning wealth, inequality, insurance, and demographic changes. This paper also contains a detailed description of the agent-based model used for the analyses. The model is calibrated to Danish data, but the insights drawn from the model are of general validity.