Model-based clustering is a popular approach for clustering multivariate data which has seen application in numerous fields. Nowadays, high-dimensional data are more and more common and the model-based clustering approach has adapted to deal with the increasing dimensionality. In particular, the development of variable selection techniques has received lot of attention and research effort in recent years. Even for small size problems, variable selection has been advocated to facilitate the interpretation of the clustering results. This review provides a summary of the methods developed for selecting relevant clustering variables in model-based clustering. The methods are illustrated by application to real-world data and existing software to implement the methods are indicated. Variable Selection Methods for Model-based Clustering