Recording from a large neuronal population of neurons is a crucial challenge to unravel how information is processed by the brain. In this review, we highlight the recent advances made in the field of “spike sorting”, which is arguably a very essential processing step to extract neuronal activity from extracellular recordings. We more specifically target the challenges faced by newly manufactured high-density multielectrode array devices (HD-MEA), e.g. Neuropixels probes. Among them, we cover in depth the prominent problem of drifts (movements of the neurons with respect to the recording devices) and the current solutions to circumscribe it. In addition, we also review recent contributions making use of deep learning approaches for spike sorting, highlighting their advantages and disadvantages. Next, we highlight efforts and advances in unifying, validating, and benchmarking spike sorting tools. Finally, we discuss the spike sorting field in terms of its open and unsolved challenges, specifically regarding scalability and reproducibility. We conclude by providing our personal view on how the future of spike sorting, calling for a community-based development and validation of spike sorting algorithms and fully automated, cloud-based spike sorting solutions for the neuroscience community.