State of the art artificial neural networks have reached incredible levels of performance, yet still, these models perform far below our expectations in terms of strong out-of-domain generalization and data efficiency. One sub-field of machine learning which has aimed to tackle both these weaknesses simultaneously is equivariant deep learning, or more generally the field of structured representation learning. However, to date, it is still unknown how to best integrate the more complex structure of the natural world into deep neural network models to realize the same efficiency and generalization benefits that equivariant models have provided for simpler group transformations. In this chapter, and this book more broadly, we introduce these core concepts, and further overview a series of recent state of the art publications in the domain of structured representation learning which attempt to directly address the limitations of modern structured representation learning methods.