The (medical) image semantic segmentation task consists of classifying each pixel of an image (or just several ones) into an instance, where each instance (or category) corresponding to a class. This task is a part of the concept of scene understanding or better explaining the global context of an image. In the medical image analysis domain, image segmentation can be used for image-guided interventions, radiotherapy, or improved radiological diagnostics. In this review, we categorize the main deep learning-based medical and non-medical image segmentation solutions into six main groups of deep architectural improvements, data synthesis-based, loss function-based improvements, sequenced models, weakly supervised, and multi-task methods and further for each group we analyzed each variant of these groups and discuss limitations of the current approaches and future research directions for semantic image segmentation. Deep Semantic Segmentation of Natural and Medical Images: A Review