State-of-the-art biostatistics methods allow for the simultaneous modelling of several correlated non-fatal disease processes over time, but there is no clear guidance on the optimal analysis in many settings. An example occurs in diabetes, where it is not known with certainty how microvascular complications of the eyes, kidneys, and nerves co-develop over time. In this paper, we propose and contrast two general model frameworks for studying complications (sequential trajectory and parallel trajectory frameworks) and review multivariate methods for their analysis, focusing on multistate and joint modelling. We illustrate these methods in a tutorial format using the long-term follow-up from the Diabetes Control and Complications Trial (DCCT) and Epidemiology of Diabetes Interventions and Complications (EDIC) study public data repository. Our illustration shows that multistate models are particularly advantageous for determining the order and timing of complications, but require discretization of the longitudinal outcomes and possibly a very complex state space process. Discretization is a possible disadvantage of multistate models in this setting. In contrast, joint models can account for variations of continuous biomarkers over time and are particularly designed for modelling complex association structures between the diabetic complications of interest and for performing dynamic predictions of an outcome of interest to inform clinical decisions (e.g., a late-stage diabetic complication). In sum, both types of models can better-inform our understanding of the complex paths and trajectories that complications can take and therefore help with decision making for patients presenting with diabetes complications.