Natural Language Processing (NLP) is revolutionising the way legal professionals and laypersons operate in the legal field. The considerable potential for NLP in the legal sector, especially in developing computational tools for various legal processes, has captured the interest of researchers for years. This survey follows the Preferred Reporting Items for Systematic Reviews and Meta-Analyses framework, reviewing 154 studies, with a final selection of 133 after manual filtering. It explores foundational concepts related to NLP in the legal domain, illustrating the unique aspects and challenges of processing legal texts, such as extensive document length, complex language, and limited open legal datasets. We provide an overview of NLP tasks specific to legal text, such as Legal Document Summarisation, legal Named Entity Recognition, Legal Question Answering, Legal Argument Mining, Legal Text Classification, and Legal Judgement Prediction. In the section on legal Language Models (LMs), we analyse both developed LMs and approaches for adapting general LMs to the legal domain. Additionally, we identify 16 Open Research Challenges, including bias in Artificial Intelligence applications, the need for more robust and interpretable models, and improving explainability to handle the complexities of legal language and reasoning.