Currently, wearable technology is present in different fields that aim to satisfy our needs in daily life, including the improvement of our health in general, the monitoring of patient health, ensuring the safety of people in the workplace or supporting athlete training. The objective of this bibliometric analysis is to examine and map the scientific advances in wearable technologies in healthcare, as well as to identify future challenges within this field and put forward some proposals to address them. In order to achieve this objective, a search of the most recent related literature was carried out in the Scopus database. Our results show that the research can be divided into two periods: before 2013, it focused on design and development of sensors and wearable systems from an engineering perspective and, since 2013, it has focused on the application of this technology to monitoring health and well-being in general, and in alignment with the Sustainable Development Goals wherever feasible. Our results reveal that the United States has been the country with the highest publication rates, with 208 articles (34.7%). The University of California, Los Angeles, is the institution with the most studies on this topic, 19 (3.1%). Sensors journal (Switzerland) is the platform with the most studies on the subject, 51 (8.5%), and has one of the highest citation rates, 1461. We put forward an analysis of keywords and, more specifically, a pennant chart to illustrate the trends in this field of research, prioritizing the area of data collection through wearable sensors, smart clothing and other forms of discrete collection of physiological data.