As the global demand for data has continued to rise exponentially, some have begun turning to the idea of semantic communication as a means of efficiently meeting this demand. Pushing beyond the boundaries of conventional communication systems, semantic communication focuses on the accurate recovery of the meaning conveyed from source to receiver, as opposed to the accurate recovery of transmitted symbols. In this survey, we aim to provide a comprehensive view of the history and current state of semantic communication and the techniques for engineering this higher level of communication. A survey of the current literature reveals four broad approaches to engineering semantic communication. We term the earliest of these approaches classical semantic information, which seeks to extend information-theoretic results to include semantic information. A second approach makes use of knowledge graphs to achieve semantic communication, and a third utilizes the power of modern deep learning techniques to facilitate this communication. The fourth approach focuses on the significance of information, rather than its meaning, to achieve efficient, goal-oriented communication. We discuss each of these four approaches and their corresponding studies in detail, and provide some challenges and opportunities that pertain to each approach. Finally, we introduce a novel approach to semantic communication, which we term context-based semantic communication. Inspired by the way in which humans naturally communicate with one another, this context-based approach provides a general, optimization-based design framework for semantic communication systems. Together, this survey provides a useful guide for the design and implementation of semantic communication systems.