The opportunity to automate and monitor the execution of legal contracts is gaining increasing interest in Business and Academia, thanks to the advent of smart contracts, blockchain technologies, and the Internet of Things. A critical issue in developing smart contract systems is the formalization of legal contracts, which are traditionally expressed in natural language with all the pitfalls that this entails. This paper presents a systematic literature review of papers for the main steps related to the transformation of a legal contract expressed in natural language into a formal specification. Key research studies have been identified, classified, and analyzed according to a four-step transformation process: (a) structural and semantic annotation to identify legal concepts in text, (b) identification of relationships among concepts, (c) contract domain modeling, and (d) generation of a formal specification. Each one of these steps poses serious research challenges that have been the subject of research for decades. The systematic review offers an overview of the most relevant research efforts undertaken to address each step and identifies promising approaches, best practices, and existing gaps in the literature.