Traditional bulk sequencing methods are limited to measuring the average signal in a group of cells, potentially masking heterogeneity, and rare populations. The single-cell resolution, however, enhances our understanding of complex biological systems and diseases, such as cancer, the immune system, and chronic diseases. However, the single-cell technologies generate massive amounts of data that are often high-dimensional, sparse, and complex, thus making analysis with traditional computational approaches difficult and unfeasible. To tackle these challenges, many are turning to deep learning (DL) methods as potential alternatives to the conventional machine learning (ML) algorithms for single-cell studies. DL is a branch of ML capable of extracting high-level features from raw inputs in multiple stages. Compared to traditional ML, DL models have provided significant improvements across many domains and applications. In this work, we examine DL applications in genomics, transcriptomics, spatial transcriptomics, and multi-omics integration, and address whether DL techniques will prove to be advantageous or if the single-cell omics domain poses unique challenges. Through a systematic literature review, we have found that DL has not yet revolutionized the most pressing challenges of the single-cell omics field. However, using DL models for single-cell omics has shown promising results (in many cases outperforming the previous state-of-the-art models) in data preprocessing and downstream analysis. Although developments of DL algorithms for single-cell omics have generally been gradual, recent advances reveal that DL can offer valuable resources in fast-tracking and advancing research in single-cell.