Due to the ongoing trend of digitalization, the importance of software for today’s society is continuously increasing. Naturally, there is also a huge interest in improving its quality, which led to a highly active research community dedicated to this aim. Consequently, a plethora of propositions, tools, and methods emerged from the corresponding efforts. One of the approaches that have become highly prominent is the concept of test-driven development (TDD) that increases the quality of created software by restructuring the development process. However, such a big change to the followed procedures is usually also accompanied by major challenges that pose a risk for the achievement of the set targets. In order to find ways to overcome them, or at least to mitigate their impact, it is necessary to identify them and to subsequently raise awareness. Furthermore, since the effect of TDD on productivity and quality is already extensively researched, this work focuses only on issues besides these aspects. For this purpose, a literature review is presented that focuses on the challenges of TDD. In doing so, challenges that can be attributed to the three categories of people, software, and process are identified and potential avenues for future research are discussed.