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Prognostic models in the context of health are a class of clinical prediction model which aim to predict the future outcome of a disease or condition. These models are essential in planning treatment and the allocation of resources. Prognostic models can ensure that treatment is delivered only when needed. Many such models have been developed using traditional statistical methods, such as logistic regression and proportional hazards. Some are routinely used in clinic. Traditional methods rely on the relevant variables being known and easy to extract; variables or features are often difficult or even impossible to extract, especially when imaging is used. Deep learning methods can automatically extract relevant features from the image. These methods have been used extensively on classification problems, detecting diseases from imaging data; however, they are less common for prognostic modelling, especially when using longitudinal data. In this thesis, I explore how deep learning can be used to develop prognostic models to predict the future course of disease using longitudinal data. After reviewing the previous methods and discussing their limitations, I develop novel methods which aim to be more accurate and clinically useful than previous methods. Throughout the thesis, I demonstrate the novel methods using colour fundus images of patients with age-related macular degeneration. I evaluated my models using current best practices for clinical prediction models. In real-world settings, the time interval between visits is unlikely to be the same each time; therefore, I present a method to account for uneven intervals between visits. I show results for one, two, and three time points to assess the added utility of additional time points and conclude that a single time point is sufficient in this situation. Finally, I develop deep survival models and present a method that accounts for both uneven time intervals and missing visits through a novel mixed-effects layer. I also show how clinical data can be incorporated into the model, although this does not significantly improve the performance. Unfortunately, all my developed models show poor calibration and require adjustment before being deployed in a clinical setting. This highlights the importance of assessing and revising the calibration of clinical prediction models. The methods presented in this thesis may be used in developing prognostic algorithms helping to deliver personalised healthcare.