In the field of machine learning, vector quantization is a category of low-complexity approaches that are nonetheless powerful for data representation and clustering or classification tasks. Vector quantization is based on the idea of representing a data or a class distribution using a small set of prototypes, and hence, it belongs to interpretable models in machine learning. Further, the low complexity of vector quantizers makes them interesting for the application of quantum concepts for their implementation. This is especially true for current and upcoming generations of quantum devices, which only allow the execution of simple and restricted algorithms. Motivated by different adaptation and optimization paradigms for vector quantizers, we provide an overview of respective existing quantum algorithms and routines to realize vector quantization concepts, maybe only partially, on quantum devices. Thus, the reader can infer the current state-of-the-art when considering quantum computing approaches for vector quantization.