‘Parentally biased favouritism’ occurs when the two parents differentially care for individual offspring or kinds of offspring. Examples in birds include brood division and differential investment by the two parents in relation to the size or sex of the offspring. This paper uses mathematical models to investigate which ideas can, in theory, explain parentally biased favouritism. One previous explanation is that the parents differ in their cost of reproduction and that the parent who consequently invests least concentrates its care on the more valuable offspring. However, a mathematical model predicts the total care given by each parent and received by each offspring, not how much each parent cares for each offspring, and hence does not explain parentally biased favouritism. Parentally biased favouritism towards particular types of offspring can be explained by a difference between the parents in the benefits of caring for a given type of offspring or in the effort incurred in providing care to a given type of offspring, but then it is extreme, with at least one of the parents providing care to only one type of offspring. Parentally biased favouritism towards particular individual offspring (brood division) can be explained by parent–offspring conflict or sexual conflict.