The adequate assessment and management of indoor air quality in healthcare facilities is of utmost importance for patient safety and occupational health purposes. This study aims to identify the recent trends of research on the topic through a systematic literature review following the preferred reporting items for systematic reviews and meta-analyses (PRISMA) methodology. A total of 171 articles published in the period 2015–2020 were selected and analyzed. Results show that there is a worldwide growing research interest in this subject, dispersed in a wide variety of scientific journals. A textometric analysis using the IRaMuTeQ software revealed four clusters of topics in the sampled articles: physicochemical pollutants, design and management of infrastructures, environmental control measures, and microbiological contamination. The studies focus mainly on hospital facilities, but there is also research interest in primary care centers and dental clinics. The majority of the analyzed articles (85%) report experimental data, with the most frequently measured parameters being related to environmental quality (temperature and relative humidity), microbiological load, CO2 and particulate matter. Non-compliance with the WHO guidelines for indoor air quality is frequently reported. This study provides an overview of the recent literature on this topic, identifying promising lines of research to improve indoor air quality in healthcare facilities.