In diabetes and other chronic lifelong diseases, it is not always known with certainty how chronic correlated non-fatal disease processes co-develop over time. It is also not obvious how to analyze this complex multivariate statistical problem. This thesis reviews and proposes methods that allow for the simultaneous modelling of several such processes. In a tutorial setting, it is shown that multistate and joint modelling approaches are useful for the overall research objective. Multistate models are found to be particularly applicable for questions surrounding the order and timing of disease-related processes. However, they require discretization of outcome data and possibly a very complex state space when more than two processes are modelled. In contrast, joint models can account for variations of continuous biomarkers over time and are particularly designed for modelling complex multivariate association structures. It would therefore be useful to combine elements of multistate and joint models, and the next part of the thesis develops this framework. Shared random effects can be used to link multistate and longitudinal processes, but most existing approaches assume that the multistate transition times are exactly observed. This renders them unsuitable for interval cohort studies, which are one of the most popular study designs for questions surrounding the natural history of complications. In interval cohort studies, participants are intermittently observed at regular intervals and are thus subject to mixed observation schemes where certain events are interval-censored and others are exactly observed. A novel shared random effects joint model for a longitudinal outcome and a multistate process under a mixed observation scheme is thus proposed. An appropriate likelihood function is defined and the model is fitted using a maximum likelihood framework with adaptive Gaussian quadrature. The model is assessed using simulation studies and is applied to 30-year data from the Diabetes Control and Complications Trial and Epidemiology of Diabetes Interventions and Complications study. The model is then extended to accommodate multiple longitudinal outcomes via Bayesian estimation using Hamiltonian Monte Carlo. In the end, it is shown that the novel joint multistate model gives greater insight into the natural history of a full complications process.