Predicting human mobility between locations is of great significance for investigating the population migration, traffic forecasting, epidemic spreading, commodity trade, social interaction and other relevant areas. The intervening opportunity (IO) model is the model established earliest from the perspective of individual choice behavior to predict human mobility. The IO model takes the total number of opportunities between the origin location and the destination as a key factor in determining human mobility, which has inspired researchers to propose many new IO class models. In this paper, we first review the research advances in the IO class models, including the IO model, radiation class models, population-weighted opportunity class models, exploratory IO class models and universal opportunity model. Among them, although the IO model has an important theoretical value, it contains parameters and has low prediction accuracy, so it is rarely used in practice. The radiation class models are built on the basis of the IO model on the assumption that the individual will choose the closest destination whose benefit is higher than the best one available in origin location. The radiation class models can better predict the commuting behavior between locations. The population-weighted opportunity class models are established on the assumption that when seeking a destination, the individual will not only consider the nearest locations with relatively large benefits, but also consider all locations in the range of alternative space. The population-weighted opportunity class models can better predict intracity trips and intercity travels. The exploratory IO class models are built on condition that the destination selected by the individual presents a higher benefit than the benefit of the origin and the benefits of the intervening opportunities. The exploratory IO class models can better predict the social interaction between individuals, intracity trips and intercity travels. The universal opportunity model is developed on the assumption that when an individual selects a destination, she/he will comprehensively compare the benefits between the origin and the destination and their intervening opportunity. The universal opportunity model presents a new universal framework for IO class models and can accurately predict the movements on different spatiotemporal scales. The IO class models have also been widely used in many fields, including predicting trip distribution in transportation science, modeling the purchasing behaviors of consumers in economics, detecting complex network communities in network science, measuring spatial interaction in economic geography and predicting infectious disease transmission in epidemiology. This paper focuses on the applications of IO class models in spatial interaction and epidemic spreading, and finally presents the discussion on the possible future research directions of these models.