The past few years have produced a series of spectacular advances in the decoding of speech from brain activity. The engine of these advances has been the acquisition of labelled data, with increasingly large datasets acquired from single subjects. However, participants exhibit anatomical and other individual differences, and datasets use varied scanners and task designs. As a result, prior work has struggled to leverage data from multiple subjects, multiple datasets, multiple tasks, and unlabelled datasets. In turn, the field has not benefited from the rapidly growing number of open neural data repositories to exploit large-scale data and deep learning. To address this, we develop an initial set of neuroscience-inspired self-supervised objectives, together with a neural architecture, for representation learning from heterogeneous and unlabelled neural recordings. Experimental results show that representations learned with these objectives generalise across subjects, datasets, and tasks, and are also learned faster than using only labelled data. In addition, we set new benchmarks for two foundational speech decoding tasks. Taken together, these methods now unlock the potential for training speech decoding models with orders of magnitude more existing data.