The paper presents a non-exhaustive survey of the literature designed to explain emergence, size and political sustainability of pay-as-you-go pension systems. It proposes a simple framework of analysis (a small open two overlapping generation economy model), around which some variants are displayed. Dictatorship of the median voter is assumed. The text is organized to answer the following questions: (i) do political equilibria with PAYG pension schemes exist, (ii) why do they emerge, (iii) what are the conditions for the participation constraint of the pension game to be verified, and finally (iv) what is the size of the pension system chosen by the median voter and how is this size influenced by an exogenous (e.g. demographic) shock.