Automated Machine Learning (AutoML) aims to identify the best-performing machine learning algorithm along with its input parameters for a given dataset and a specific machine learning task. This is a challenging problem, as the process of finding the best model and tuning it for a particular problem at hand is both time-consuming for a data scientist and computationally expensive. In this survey, we focus on unsupervised learning, and we turn our attention on AutoML methods for clustering. We present a systematic review that includes many recent research works for automated clustering. Furthermore, we provide a taxonomy for the classification of existing works, and we perform a qualitative comparison. As a result, this survey provides a comprehensive overview of the field of AutoML for clustering. Moreover, we identify open challenges for future research in this field.