Due to the process of globalization, companies are obligated to observe corporate social responsibility and best practices from a sustainability approach towards their stakeholders and society. The explicit aim is to determine the relevance of the corporate social responsibility (CSR) and its relationship with sustainability, in order to establish trends and future lines of research. The evolution of global research on this subject has been studied from 2001 to 2018. For this purpose, a bibliometric analysis of 1832 articles has been applied, obtaining results of the scientific productivity of the journals, authors, institutions, and countries that contribute to this research. Evidence shows a growing interest in studying the relationship between socially responsible practices and the dimension of sustainability. The main category is Business, Management, and Accounting. The most productive journals are the Journal of Business Ethics and Sustainability. The authors with the most articles are García-Sánchez, Moneva, and Moratis, while Kolk is the most cited. The most prolific institution is the University of Salamanca. The United States is the country with the most publications and quotes. France and China are the countries with the largest number of international collaborations in their work. Global research has been on an upward trend with optimal publication rates in recent years.