Deep neural networks can achieve great successes when presented with large data sets and sufficient computational resources. However, their ability to learn new concepts quickly is limited. Meta-learning is one approach to address this issue, by enabling the network to learn how to learn. The field of Deep Meta-Learning advances at great speed, but lacks a unified, in-depth overview of current techniques. With this work, we aim to bridge this gap. After providing the reader with a theoretical foundation, we investigate and summarize key methods, which are categorized into i)~metric-, ii)~model-, and iii)~optimization-based techniques. In addition, we identify the main open challenges, such as performance evaluations on heterogeneous benchmarks, and reduction of the computational costs of meta-learning.