Artificial intelligence, deep convolutional neural networks, and deep learning are all niche terms that are increasingly appearing in scientific presentations as well as in the general media. In this review, we focus on deep learning and how it is applied to microscopy image data of cells and tissue samples. Starting with an analogy to neuroscience, we aim to give the reader an overview of the key concepts of neural networks, and an understanding of how deep learning differs from more classical approaches for extracting information from image data. We aim to increase the understanding of these methods, while highlighting considerations regarding input data requirements, computational resources, challenges, and limitations. We do not provide a full manual for applying these methods to your own data, but rather review previously published articles on deep learning in image cytometry, and guide the readers toward further reading on specific networks and methods, including new methods not yet applied to cytometry data.