Objectives: This study aims to systematically review the literature on the computational processing of the language of pain, whether generated by patients or physicians, identifying current trends and challenges. Methods: Following the PRISMA guidelines, a comprehensive literature search was conducted to select relevant studies on the computational processing of the language of pain and answer pre-defined research questions. Data extraction and synthesis were performed to categorize selected studies according to their primary purpose and outcome, patient and pain population, textual data, computational methodology, and outcome targets. Results: Physician-generated language of pain, specifically from clinical notes, was the most used data. Tasks included patient diagnosis and triaging, identification of pain mentions, treatment response prediction, biomedical entity extraction, correlation of linguistic features with clinical states, and lexico-semantic analysis of pain narratives. Only one study included previous linguistic knowledge on pain utterances in their experimental setup. Most studies targeted their outcomes for physicians, either directly as clinical tools or as indirect knowledge. The least targeted stage of clinical pain care was self-management, in which patients are most involved. The least studied dimensions of pain were affective and sociocultural. Only two studies measured how physician performance on clinical tasks improved with the inclusion of the proposed algorithm. Discussion: This study found that future research should focus on analyzing patient-generated language of pain, developing patient-centered resources for self-management and patient-empowerment, exploring affective and sociocultural aspects of pain, and measuring improvements in physician performance when aided by the proposed tools.