Semantic communication is an emerging research area that has gained a wide range of attention recently. Despite this growing interest, there remains a notable absence of a comprehensive and widely-accepted framework for characterizing semantic communication. This paper introduces a new conceptualization of semantic communication and formulates two fundamental problems, which we term language exploitation and language design . Our contention is that the challenge of language design can be effectively situated within the broader framework of joint source-channel coding theory, underpinned by a comprehensive end-to-end distortion metric. To tackle the language exploitation problem, we put forth three approaches: semantic encoding, semantic decoding, and a synergistic combination of both in the form of combined semantic encoding and decoding. Furthermore, we establish the semantic distortion-cost region as a critical framework for assessing the language exploitation problem. For each of the three proposed approaches, the achievable distortion-cost region is characterized. Overall, this paper aims to shed light on the intricate dynamics of semantic communication, paving the way for a deeper understanding of this evolving field.