Certain ascertainment schemes are often used to recruit the study subjects in genetic studies in order to enhance the study feasibility. It could raise potential problems such as biased inference. Efforts have been made to correct the ascertainment bias by integrating ascertainment information into models. Recently, it has been noted that the past efforts may not be enough due to parameter heterogeneity, which probably exists in a complex genetic trait. In this review, we summarize the current understanding of the ascertainment problems and correction procedures and remaining challenges.