The amount of data processed in the cloud, the development of Internet-of-Things (IoT) applications, and growing data privacy concerns force the transition from cloud-based to edge-based processing. Limited energy and computational resources on edge push the transition from traditional von Neumann architectures to In-memory Computing (IMC), especially for machine learning and neural network applications. Network compression techniques are applied to implement a neural network on limited hardware resources. Quantization is one of the most efficient network compression techniques allowing to reduce the memory footprint, latency, and energy consumption. This paper provides a comprehensive review of IMC-based Quantized Neural Networks (QNN) and links software-based quantization approaches to IMC hardware implementation. Moreover, open challenges, QNN design requirements, recommendations, and perspectives along with an IMC-based QNN hardware roadmap are provided.