This thesis explores, develops and implements modelling strategies for studying relationships between childhood growth and later health, focusing primarily on the relationship between the development of body mass index (BMI) in childhood and later obesity. Existing growth models are explored, though found to be inflexible and potentially inadequate. Alternative approaches using parametric and nonparametric modelling are investigated. A distinction between balanced and unbalanced data structure is made because of the ways in which missing data can be addressed. A dataset of each type is used for illustration: the Stockholm Weight Development Study (SWEDES) and the Uppsala Family Study (UFS). The focus in each application is obesity, with the first examining how the adiposity rebound (AR), and the second how the adiposity peak (AP) in infancy, relate to later adiposity. In each case a two-stage approach is used. Subject-specific cubic smoothing splines are used in SWEDES to model childhood BMI and estimate the AR for each subject. As childhood BMI data are balanced, missingness can be dealt with via mUltiple imputation. The relationship between the AR and late-adolescent adiposity is then explored via linear and logistic regression, with both the age and BMI at AR found to be strongly and independently associated with late-adolescent adiposity. In the UFS, where childhood BMI data are unbalanced, penalised regression splines are used within a mixed model framework to model childhood BMI and estimate the AP for each subject. The data correlations induced by the family structure of the observations are addressed by fitting multilevel models in the second stage. Both age and BMI at AP are found to be positively associated with later adiposity. The two nonparametric modelling approaches are found to be effective and flexible. Whilst the thesis concentrates on BMI development in childhood and later adiposity, the techniques employed, both in terms the modelling of growth and the relating of the derived features to the outcomes, are far more widely applicable.