To tackle the uncertainties in life, a model that can efficiently convert qualitative concepts and quantitative values is essential. This model is referred to as a qualitative-quantitative uncertainty model. The conventional membership function provides a fixed membership degree that is incompatible with the fuzziness and randomness of qualitative concepts when a certain element of the theoretical domain is inputted. To address this issue, Academician Li introduced the cloud model, which is a qualitative-quantitative uncertainty model created for converting between qualitative and quantitative values. Unlike the traditional membership function, the cloud model generates a set of random numbers with a stable tendency that better captures the fuzziness and randomness of the qualitative concept when an element of the theoretical domain is inputted. In this paper, the background and fundamental concepts of cloud models are initially presented. Afterwards, we delve into the advancements of cloud models in various fields such as controller, data mining, and reliability. Through these discussions, the paper showcases the significant role that cloud models can play in resolving qualitative and quantitative conversion issues across different domains. The three numerical characteristics of cloud models are then described in detail, as well as cloud generator, virtual cloud and other cloud model related algorithms. Finally, some statistical properties of cloud models are discussed, as well as the current problems and future research directions.