We live in a world replete with opportunities to overeat highly calorific, palatable foods - yet not everyone becomes obese. Why? We propose that individuals show differences in appetitive traits (e.g. food cue responsiveness, satiety sensitivity) that manifest early in life and predict their eating behaviours and weight trajectories. What determines these traits? Parental feeding restriction is associated with higher child adiposity, pressure to eat with lower adiposity, and both strategies with less healthy eating behaviours, while authoritative feeding styles coincide with more positive outcomes. But, on the whole, twin and family studies argue that nature has a greater influence than nurture on adiposity and eating behaviour, and behavioural investigations of genetic variants that are robustly associated with obesity (e.g. FTO) confirm that genes influence appetite. Meanwhile, a growing body of neuroimaging studies in adults, children and high risk populations suggests that structural and functional variation in brain networks associated with reward, emotion and control might also predict appetite and obesity, and show genetic influence. Together these different strands of evidence support a biobehavioural risk model of obesity development. Parental feeding recommendations should therefore acknowledge the powerful - but modifiable - contribution of genetic and neurological influences to children's eating behaviour.