Artificial intelligence systems that have become the core driving force for the development of human society are widely used to solve various challenges in the real world in an unprecedented way. With the rapid popularization of artificial intelligence systems in all walks of life, the trustworthiness of artificial intelligence systems is becoming more and more worrying, and the main reason is that the trustworthiness of traditional software systems is not enough to fully describe the trustworthiness of artificial intelligence systems. The research on the trustworthy artificial intelligence systems is urgent. At present, there have been a large number of relevant studies, and each has its own emphasis. However, it lacks a holistic and systematic understanding. This research is a tertiary study with the existing secondary research as the research object, aiming to reveal the research status of quality attributes and practices related to the trustworthiness of artificial intelligence systems as well as to establish a more comprehensive trustworthiness framework. This study collected, organized and analyzed 34 secondary studies published until March 2022. We identified 21 quality attributes and related trustworthy measurement methods and assurance practices. We found that existing research mainly focused on security and privacy, whilst it lacks extensive and in-depth research on other quality attributes. There are two research directions that require interdisciplinary collaboration needing more attention in future research. On the one hand, the artificial intelligence system is essentially a software system, and its trustworthiness as a software system is worthy of cooperation between artificial intelligence and software engineering experts. On the other hand, artificial intelligence is the human exploration of machine anthropomorphism and the research on how to ensure the trustworthiness of the machine in the social environment from the system level, such as how to satisfy humanism, is worthy of cooperation between artificial intelligence and social science experts.