This article conducts a systematic review of the literature, which seeks to present opportunities and trends in fostering creativity in science and engineering. The literature review is based on four phases: to identify eligible articles, screen and classify the selected documents, analyse the content and the citations, and report the findings and scopes for future research. To facilitate the topic's comprehension, the authors also include a theoretical background that centres on creativity models and theories. Finally, the authors present a classification of contributions into two groups related to 1) the practices for promoting creativity in science and engineering and 2) research trends in fostering creativity in these areas. Results show that creativity is a crucial skill for science and engineering professionals and an essential ability in the design process, especially to achieve innovative and potential impacts for humanity's well-being. Likewise, the authors observe how teachers, researchers, students, and organisations of professionals agree on the need to foster creativity from education, reflecting on the growth of the contributions oriented to this goal. Mixing knowledge areas, using problems and projects, and promoting skills like group learning, problem-solving, project management, autonomy, and idea generation are some characteristics of new proposals.