The monaural speech source separation problem is an important application in the signal processing field. But recent interaction of deep learning algorithms with signal processing achieves remarkable performance improvement for speech source separation problems. This paper explores the numerous state-of-the-art deep learning-based monaural speech source separation algorithms in the timefrequency (T-F), time, and hybrid domains. The motivation, algorithm, and framework of different deep learning models for monaural speech source separation are analyzed. The benchmarked algorithms in the T-F domain can be categorized as deep neural networks (DNN), clustering, permutation, multi-task learning, computational auditory sense analysis (CASA), and phase reconstruction-based techniques, whereas the state-of-the-art time-domain approaches can be categorized as CNN, RNN, multi-scale fusion (MSF), and transformer-based techniques. The end-to-end post filter (E2EPF) is a hybrid algorithm combining T-F and time-domain works to achieve enhanced results. Time-domain models have shown improvement in separation performance compared to the T-F and hybrid domain models with small model sizes. Methods in T-F, time, and hybrid domains are compared using 𝑆𝐷𝑅, 𝑆𝐼 − 𝑆𝐷𝑅, 𝑆𝐼 − 𝑆𝑁𝑅, PESQ, and 𝑆𝑇𝑂𝐼 as quality assessment metrics on some benchmark datasets.