A variety of methods have been applied to the architectural configuration and learning or training of artificial deep neural networks (DNN). These methods play a crucial role in the success or failure of the DNN for most problems and applications. Evolutionary algorithms (EAs) are gaining momentum as a computationally feasible method for the automated optimization of DNNs. Neuroevolution is a term, which describes these processes of automated configuration and training of DNNs using EAs. While many works exist in the literature, no comprehensive surveys currently exist focusing exclusively on the strengths and limitations of using neuroevolution approaches in DNNs. Absence of such surveys can lead to a disjointed and fragmented field preventing DNNs researchers potentially adopting neuroevolutionary methods in their own research, resulting in lost opportunities for wider application within real-world deep learning problems. This article presents a comprehensive survey, discussion, and evaluation of the state-of-the-art in using EAs for architectural configuration and training of DNNs. This article highlights the most pertinent current issues and challenges in neuroevolution and identifies multiple promising future research directions. Impact Statement—The concept of deep learning originated from the study of artificial neural networks (ANNs). ANNs have achieved extraordinary results in a variety of diverse application areas. Numerous methods have been applied to the architectural configuration and learning or training of artificial DNN and these methods play a crucial role in the success or failure of the DNN for most problems and applications. Recently, EAs have been gaining momentum as a computationally feasible method (called neuroevolution) for the automated configuration and learning or training of DNNs. This article reviews over 170 recent scientific papers describing how major EAs paradigms are being applied by researchers to the configuration and optimization of multiple DNNs. By articulating a clear understanding of the context, state-of-the-art, and feasibility of Neuroevolution, researchers in AI, EAs, and DNN will benefit from this article. The impact of this article comes from contributing toward enhancing research capacity, knowledge, and skills for researchers currently working in neuroevolution and actively engaging those considering becoming involved in this area.