The lack of user engagement, the absence of user feedback, incomplete and continuously changing user requirements are among the critical concerns that cause projects to fail. User-centered design (UCD) and agile software development are two iterative approaches that have been proposed to overcome such concerns. UCD is a design process focusing on user research, user interface design and usability evaluation. Introduced by software engineering practitioners, agile refers to a number of iterative and incremental software development practices that emphasize people's needs, communication between developers and stakeholders and the ability to adapt to change. In both the agile and UCD communities, however, a full understanding of user requirements is often seen as incompatible with early and quick development iterations. We performed a literature review aiming to identify how agile teams have integrated UCD tools into their agile software development process to a better understanding of the user requirements without losing sight of the agile values and principles. UCD tools adaptations and minimal-upfront design applied in agile development are among the approaches discovered in this study. The findings could lead to a comprehensive user-centric software engineering that will overcome inherent problems faced by agile teams to understand user needs, priorities and goals.