The problem of dealing with misreported data is very common in a wide range of contexts and for different reasons. This has been and still is an important issue for data analysts and statisticians as not accounting for it could led to biased estimates and conclusions, and in many cases that would have implications in a posterior decision making process, as we all have seen in the current worldwide Covid-19 pandemic. In the last few years, many approaches have been proposed in the literature to accomodate data presenting this issue, especially in the fields of epidemiology and public health but also in other areas as social science. In this work, a comprehensive review of the recently proposed methods based on mixture models for longitudinal data (correlated and uncorrelated) is presented and several examples of application are discussed, including several approaches to the burden of Covid-19 infection cases in Spain and different approaches to deal with underreported registries of human papillomavirus infections and genital warts in Catalunya