Deep learning has recently gained immense popularity in the Earth sciences as it enables us to formulate purely data-driven models of complex Earth system processes. Deep learning-based weather prediction (DLWP) models have made significant progress in the last few years, achieving forecast skills comparable to established numerical weather prediction (NWP) models with comparatively lesser computational costs. In order to train accurate, reliable, and tractable DLWP models with several millions of parameters, the model design needs to incorporate suitable inductive biases that encode structural assumptions about the data and modelled processes. When chosen appropriately, these biases enable faster learning and better generalisation to unseen data. Although inductive biases play a crucial role in successful DLWP models, they are often not stated explicitly and how they contribute to model performance remains unclear. Here, we review and analyse the inductive biases of six state-of-the-art DLWP models, involving a deeper look at five key design elements: input data, forecasting objective, loss components, layered design of the deep learning architectures, and optimisation methods. We show how the design choices made in each of the five design elements relate to structural assumptions. Given recent developments in the broader DL community, we anticipate that the future of DLWP will likely see a wider use of foundation models – large models pre-trained on big databases with self-supervised learning – combined with explicit physics-informed inductive biases that allow the models to provide competitive forecasts even at the more challenging subseasonal-to-seasonal scales.