Tertiary education institutions aim to prepare their computer science and software engineering students for working life. While much of the technical principles are covered in lower-level courses, team-based capstone projects are a common way to provide students with hands-on experience and teach soft skills. This paper explores the characteristics of software engineering capstone courses presented in the literature. The goal of this work is to understand the pros and cons of different approaches by synthesising the various aspects of software engineering capstone courses and related experiences. In a systematic literature review for 2007-2022, we identified 127 primary studies. These studies were analysed based on their presented course characteristics and the reported course outcomes. The characteristics were synthesised into a taxonomy consisting of duration, team sizes, client and project sources, project implementation, and student assessment. We found out that capstone courses generally last one semester and divide students into groups of 4-5 where they work on a project for a client. For a slight majority of courses, the clients are external to the course staff and students are often expected to produce a proof-of-concept level software product as the main end deliverable. The courses also offer versatile assessments for students throughout the project. This paper provides researchers and educators with a classification of characteristics of software engineering capstone courses based on previous research. We further synthesise insights on the reported outcomes of capstone courses. Our review study aims to help educators to identify various ways of organising capstones and effectively plan and deliver their own capstone courses. The characterisation also helps researchers to conduct further studies on software engineering capstones.