Most models of family transfers consider only two generations and focus on two motives : altruism and exchange. They also assume perfect substitution between inter vivos financial transfers and bequests to children. On the contrary, this survey of recent developments in the literature emphasizes the strong heterogeneity of downward financial transfers and motives for these transfers over the life-cycle. In face of the empirical failure of standard models in developed countries (these models may perform better in less developed countries or in old Europe), it also advocates "mixed" motivations of transfers, such as strategic altruism, models with endogenous heterogeneous behavioral regimes (Becker, Cigno), and especially indirect reciprocities between three generations, which lead to the replication of the same type of transfer from one generation to the next. Indirect reciprocities appear able to accommodate several empirical puzzles : they are thus compatible (against altruism) with small compensatory effects of transfers both between and within generations, and (against exchange) with the lack of parents' observable counterpart to financial or time support given by their children. They also predict "3rd generation effects" - transfers between parents and children being determined by grandparents' transfers or again grandchildren's characteristics - which appear corroborated by (mainly French or U.S.) available evidence. We thus face the challenge of innovative modelling of indirect reciprocities within the framework of individual forward-looking rationality.