Multivariate time series (MTS) are captured in a great variety of real-world applications. However, analysing and modeling the data for classification and forecasting purposes can become very challenging if values are missing in the data set. The need for imputation methods, to fill the gaps in MTS, is well known. Thus, a great variaty of algorithms for solving this task has been proposed in the literature. However, the research community is constantly working on the development of advanced algorithms, that fulfill the special requirements of multidimensional temporal data, since most of the existing imputation methods treat MTS as ordinary structured data and fail to model the temporal relationships within and between sequences of observations. The main emphasis of MTS imputation research is currently put on deep learning (DL) models, especially those making use of generative adversarial networks (GANs). In our survey, we present our categorization of imputation algorithms, especially of GAN-models. We included eighteen different GAN-models designed for the MTS imputation task, which we introduce in detail. We provide a comparison of the models including their performance regarding MTS imputation, based on our findings in the literature. The following points can be considered the most important findings from our survey: The research on GAN-based imputation models for MTS has gained momentum in the last years across different domains, therewhile showing the effectiveness of these methods. The latest trend in the research area is the incorporation of attention mechanisms into the algorithms. Nevertheless, there are open research challenges, e.g. the transferability of models across data sets from different domains.