The underrepresentation of certain groups in computing has led to increasing efforts to develop computing curricula that is responsive and relevant to a more diverse group of learners. The current paper used a Quick Scoping Review methodology to identify research that has implemented and evaluated culturally responsive and relevant K-12 computing curricula, and to understand how they have been designed, the methods used for evaluation, and the factors affecting their success. In total, 12 papers were included in the review, and all were from a United States setting. Successes included changing learners' attitudes towards computing and increased learning gains. Key factors in the implementation of the curricula were teacher confidence and understanding of the socio-political context of computing, opportunities provided for collaboration and sharing knowledge and opinions, and allowing time for difficult discussions without oversimplifying the issues. The review identifies important lessons to be learned for educators around the world who are aiming to increase diversity in representation in computing in their schools.