Multi-state models can be used to analyse processes where change of status over time is of interest. In medical research, processes are commonly defined by a set of living states and a dead state. Transition times between living states are often interval censored. In this case, models are usually formulated in a Markov processes framework. The likelihood function is then constructed using transition probabilities. Models are specified using proportional hazards for the effect of covariates on transition intensities. Time-dependency is usually defined by parametric models, which can represent a strong model assumption. Semiparametric hazards specification with splines is a more flexible method for modelling time-dependency in multi-state models. Penalised maximum likelihood is used to estimate these models. Selecting the optimal amount of smoothing is challenging as the problem involves multiple penalties. This thesis aims to develop methods to estimate multi-state models with splines for interval-censored data. We propose a penalised likelihood method to estimate multi-state models that allow for parametric and semiparametric hazards specifications. The estimation is based on a scoring algorithm, and a grid search method to estimate the smoothing parameters. This method is shown using an application to ageing research. Furthermore, we extend the proposed method by developing a computationally more efficient method to estimate multi-state models with splines. For this extension, the estimation is based on a scoring algorithm, and an automatic smoothing parameters selection. The extended method is illustrated with two data analyses and a simulation study.