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The modelling of Electronic Health Records (EHRs) has the potential to drive more efficient allocation of healthcare resources, enabling early intervention strategies and advancing personalised healthcare. However, EHRs are challenging to model due to their realisation as noisy, multi-modal data occurring at irregular time intervals. To address their temporal nature, we treat EHRs as samples generated by a Temporal Point Process (TPP), enabling us to model what happened in an event with when it happened in a principled way. We gather and propose neural network parameterisations of TPPs, collectively referred to as Neural TPPs. We perform evaluations on synthetic EHRs as well as on a set of established benchmarks. We show that TPPs significantly outperform their non-TPP counterparts on EHRs. We also show that an assumption of many Neural TPPs, that the class distribution is conditionally independent of time, reduces performance on EHRs. Finally, our proposed attention-based Neural TPP performs favourably compared to existing models, whilst aligning with real world interpretability requirements, an important step towards a component of clinical decision support systems.