Background: Electronic health records (EHRs) are a valuable resource for data-driven medical research. However, the presence of protected health information (PHI) makes EHRs unsuitable to be shared for research purposes. De-identification, i.e. the process of removing PHI is a critical step in making EHR data accessible. Natural language processing has repeatedly demonstrated its feasibility in automating the de-identification process. Objectives: Our study aims to provide systematic evidence on how the de-identification of clinical free text has evolved in the last thirteen years, and to report on the performances and limitations of the current state-of-the-art systems. In addition, we aim to identify challenges and potential research opportunities in this field. Methods: A systematic search in PubMed, Web of Science and the DBLP was conducted for studies published between January 2010 and February 2023. Titles and abstracts were examined to identify the relevant studies. Selected studies were then analysed in-depth, and information was collected on de-identification methodologies, data sources, and measured performance. Results: A total of 2125 publications were identified for the title and abstract screening. 69 studies were found to be relevant. Machine learning (37 studies) and hybrid (26 studies) approaches are predominant, while six studies relied only on rules. Majority of the approaches were trained and evaluated on public corpora. The 2014 i2b2/UTHealth corpus is the most frequently used (36 studies), followed by the 2006 i2b2 (18 studies) and 2016 CEGS N-GRID (10 studies) corpora.