Medical computer-aided diagnosis systems are essential applications that help doctors speed up, standardize, and improve disease prediction quality. Nevertheless, it is hard to implement a high-accuracy diagnosis system due to complex medical data structures that are hard to interpret even by an experienced radiologist, lack of the labeled data, and the high-resolution three-dimensional nature of the data. Meanwhile, modern deep learning methods achieved a significant breakthrough in various computer vision tasks. Thus, the same methods began to gain popularity in the community that works on the computer-aided systems implementation. Most modern diagnosis systems work with three-dimensional medical images that cannot be processed by traditional two-dimensional convolutional neural networks to get high enough prediction results. Hence, medical research introduced new methods that use three-dimensional neural networks to work with medical images. Even though these networks are usually an adapted version of state-of-the-art two-dimensional networks, they still have their specifics and modifications that help achieve human-level accuracy and should be considered separately. This article overviews the three-dimensional convolutional neural networks and how they are different from their two-dimensional versions. Moreover, the article examines the most influenced systems that achieve human-level accuracy in predicting the specific disease. The networks discussed in the perspective of two basic tasks: segmentation and classification. That is because the simple end-to-end classification neural networks usually do not work well on the available amount of data in the medical domain.