Deep neural networks have established themselves as one of the most promising machine learning techniques. Training such models at large scales is often parallelized, giving rise to the concept of distributed deep learning. Distributed techniques are often employed in training large models or large datasets either out of necessity or simply for speed. Quantum machine learning, on the other hand, is the interplay between machine learning and quantum computing. It seeks to understand the advantages of employing quantum devices in developing new learning algorithms as well as improving the existing ones. A set of architectures that are heavily explored in quantum machine learning are quantum neural networks. In this review, we consider ideas from distributed deep learning as they apply to quantum neural networks. We find that the distribution of quantum datasets shares more similarities with its classical counterpart than does the distribution of quantum models, though the unique aspects of quantum data introduces new vulnerabilities to both approaches. We review the current state of the art in distributed quantum neural networks, including recent numerical experiments and the concept of circuit cutting.