Quality requirements deal with how well a product should perform the intended functionality, such as start-up time and learnability. Researchers argue they are important and at the same time studies indicate there are deficiencies in practice. Our goal is to review the state of evidence for quality requirements. We want to understand the empirical research on quality requirements topics as well as evaluations of quality requirements solutions. We used a hybrid method for our systematic literature review. We defined a start set based on two literature reviews combined with a keyword-based search from selected publication venues. We snowballed based on the start set. We screened 530 papers and included 84 papers in our review. Case study method is the most common (43), followed by surveys (15) and tests (13). We found no replication studies. The two most commonly studied themes are (1) differentiating characteristics of quality requirements compared to other types of requirements, (2) the importance and prevalence of quality requirements. Quality models, QUPER, and the NFR method are evaluated in several studies, with positive indications. Goal modeling is the only modeling approach evaluated. However, all studies are small scale and long-term costs and impact are not studied. We conclude that more research is needed as empirical research on quality requirements is not increasing at the same rate as software engineering research in general. We see a gap between research and practice. The solutions proposed are usually evaluated in an academic context and surveys on quality requirements in industry indicate unsystematic handling of quality requirements.