Recent advances in deep learning have led to increased interest in solving high-efficiency end-to-end transmission problems using methods that employ the nonlinear property of neural networks. These methods, we call semantic coding, extract semantic features of the source signal across space and time, and design source-channel coding methods to transmit these features over wireless channels. Rapid progress has led to numerous research papers, but a consolidation of the discovered knowledge has not yet emerged. In this article, we gather ideas to categorize the expansive aspects on semantic coding as two paradigms, i.e., explicit and implicit semantic coding. We first focus on those two paradigms of semantic coding by identifying their common and different components in building semantic communication systems. We then focus on the applications of semantic coding to different transmission tasks. Our article highlights the improved quality, flexibility, and capability brought by semantic coded transmission. Finally, we point out future directions.