In the field of systems biology, experimental biology and mathematical modelling go hand in hand. When experimental biologists start using new techniques, mathematical modellers have to respond to the challenges they create. Recently, experimental biologists have widely adopted next-generation sequencing techniques that enable transcriptome measurements on the single-cell level. However, whenever a cell is measured it is destroyed: thus each cell can be measured only once and, hence, cannot be followed over time. The resulting data is, therefore, not a time series, but rather a collection of individual measurements at different times. Building dynamical models from single-cell measurements constitutes a challenging scenario that is yet to receive much attention. Dynamical models have great potential to abstract these large datasets and extract vital information on cell mechanisms and how their malfunctions may lead to diseases. This project considers two different modelling paradigms applicable to single-cell data. First, it develops and analyses a modelling approach based on estimating cell trajectories from the data and fitting the dynamical models to the estimated trajectories. Secondly, it considers methods based on tracking the evolution of the distribution of cells between measurement times. The overall aim is to increase the accuracy of cell dynamics models, by enabling model inference from single-cell data. Such data should provide a far more detailed picture of cellular processes than that which is obtained from traditional bulk time series measurements. The increased accuracy stands to directly benefit biological and biomedical research, and ultimately also patients with genetic disorders. We will use the developed modelling framework to analyse the effect of LRRK2 and PINK1 mutations on the dynamics of stem cells differentiating to dopaminergic neurons, and the aging of neurons. We expect these results to explain how these mutations lead to Parkinson disease.