During the last few decades, a convolutional neural network (CNN) has become a very popular deep learning technique in automatic tumor segmentation of medical images of cancer patients. However, unlike for semantic segmentation of regular photographs, there are few publicly available datasets that can be used to train a CNN to perform tumor segmentation in medical images. Consequently, it is difficult to compare these methods or tell how well they should work for a specific combination of cancer type and imaging modality when trained with a certain amount of data. To answer this question, we analyzed 325 recent articles about CNNs trained for tumor segmentation in order to give a comprehensive overview of the current state of research. The articles study several different types of cancer, including brain tumors and breast, liver, lung, skin, head and neck, prostate, thyroid, cervical, colorectal, pancreatic, kidney, and bladder cancer, imaged with magnetic resonance imaging (MRI), computed tomography, positron emission tomography, ultrasound, and other similar modalities. According to our analysis, the most popular CNN for tumor segmentation is U-Net and its new modifications. Conversely, Mask region-based CNNs are rarely used outside of MRI images. Out of the other CNN designs, SegNet and DeepLabV3 are most common but still significantly less studied than U-Net. Furthermore, several methods have not yet been tested for rarer types of cancer.