Conventional multiview clustering seeks to partition data into respective groups based on the assumption that all views are fully observed. However, in practical applications, such as disease diagnosis, multimedia analysis, and recommendation system, it is common to observe that not all views of samples are available in many cases, which leads to the failure of the conventional multiview clustering methods. Clustering on such incomplete multiview data is referred to as incomplete multiview clustering (IMC). In view of the promising application prospects, the research of IMC has noticeable advances in recent years. However, there is no survey to summarize the current progresses and point out the future research directions. To this end, we review the recent studies of IMC. Importantly, we provide some frameworks to unify the corresponding IMC methods and make an in-depth comparative analysis for some representative methods from theoretical and experimental perspectives. Finally, some open problems in the IMC field are offered for researchers. The related codes are released at https://github.com/DarrenZZhang/Survey_IMC.