Abstract Recent years have seen the massive migration of enterprise applications to the cloud. One of the challenges posed by cloud applications is Quality-of-Service (QoS) management, which is the problem of allocating resources to the application to guarantee a service level along dimensions such as performance, availability and reliability. This paper aims at supporting research in this area by providing a survey of the state of the art of QoS modeling approaches suitable for cloud systems. We also review and classify their early application to some decision-making problems arising in cloud QoS management.