Many small passerines are resident in forests with very cold winters. Considering their size and the adverse conditions, this is a remarkable feat that requires optimal energy management in several respects, for example regulation of body fat reserves, food hoarding and night-time hypothermia. Besides their beneficial effect on survival, these behaviours also entail various costs. The scenario is complex with many potentially important factors, and this has made 'the little bird in winter' a popular topic for theoretic modellers. Many predictions could have been made intuitively, but models have been especially important when many factors interact. Predictions that hardly could have been made without models include: (i) the minimum mortality occurs at the fat level where the marginal values of starvation risk and predation risk are equal; (ii) starvation risk may also decrease when food requirement increases; (iii) mortality from starvation may correlate positively with fat reserves; (iv) the existence of food stores can increase fitness substantially even if the food is not eaten; (v) environmental changes may induce increases or decreases in the level of reserves depending on whether changes are temporary or permanent; and (vi) hoarding can also evolve under seemingly group-selectionistic conditions.