Software process improvement programs are partly founded on software measurement. However, despite their importance, it has been pointed out in the literature that many students are leaving the academic world without the necessary skills to conduct this kind of process. This can be understood by people’s attitudes to this process which is regarded as time-consuming and difficult to understand—factors that explain the lack of interest in it during a student’s academic life. In light of this, the application of serious games or gamification can show useful alternative ways of meeting this need, because the strategies they involve are well accepted by students and have a motivational and engaging effect on them. The objective of this work is to discover different approaches to the teaching of software measurement and software process improvement through gamification projects and serious games. This involves carrying out a systematic review of the literature, which is aimed at characterizing the state-of-the-art on the use of methods related to gamification and serious games in the abovementioned subjects. We conducted a systematic review of the literature to identify primary studies that address the use, planning, or evaluation of gamification, serious games, their features, and game mechanics in software engineering. We located 137 primary studies, published between 2000 and 2019. Although the use of serious games and gamification in software engineering is not recent, there still remains a large area to be explored, especially in software process improvement and software measurement. The study expands and advances the research on how serious games and gamification proposals can be used for teaching software measurement in the context of software process improvement programs by conducting a systematic review of the literature.