Objective.Deep learning is increasingly permeating neuroscience, leading to a rise in signal-processing applications for extracellular recordings. These signals capture the activity of small neuronal populations, necessitating 'spike sorting' to assign action potentials (spikes) to their underlying neurons. With the rise in publications delving into new methodologies and techniques for deep learning-based spike sorting, it is crucial to synthesise these findings critically. This survey provides an in-depth evaluation of the approaches, methodologies and outcomes presented in recent articles, shedding light on the current state-of-the-art.Approach.Twenty-four articles published until December 2023 on deep learning-based spike sorting have been examined. The proposed methods are divided into three sub-problems of spike sorting: spike detection, feature extraction and classification. Moreover, integrated systems, i.e., models that detect spikes and extract features or do classification within a single network, are included.Main Results.Although most algorithms have been developed for single-channel recordings, models utilising multi-channel data have already shown promising results, with efficient hardware implementations running quantised models on ASICs and FPGAs. Convolutional neural networks have been used extensively for spike detection and classification as the data can be processed spatiotemporally while maintaining low-parameter models and increasing generalisation and efficiency. Autoencoders have been mainly utilised for dimensionality reduction, enabling subsequent clustering with standard methods. Also, integrated systems have shown great potential in solving the spike sorting problem from end to end.Significance.This survey explores recent articles on deep learning-based spike sorting and highlights the capabilities of deep neural networks in overcoming associated challenges, but also highlights potential biases of certain models. Serving as a resource for both newcomers and seasoned researchers in the field, this work provides insights into the latest advancements and may inspire future model development.