Liver cancer remains a major global health burden due to its rising incidence and high mortality. Computed tomography (CT) is central to diagnosis and treatment planning, providing detailed anatomical and temporal information. In recent years, deep learning techniques, especially convolutional neural networks (CNNs) and Transformer-based models, have demonstrated strong potential in CT imaging, enabling automated tumor detection, segmentation, and characterization. These advances promise early diagnosis and precision medicine, though challenges such as limited annotated datasets, imaging variability, and barriers to clinical adoption remain. To capture recent progresses, we conducted a structured literature search in PubMed, IEEE Xplore, ScienceDirect, and SpringerLink for studies published between January 2021 and June 2025. Search terms combined three domains: deep learning/artificial intelligence (AI), liver cancer/hepatocellular carcinoma, and CT imaging. Eligible studies included original research applying deep learning to hepatic oncology CT tasks with quantitative evaluation, while the studies lacking methodological transparency or validation were excluded. Unlike prior broad reviews, this work specifically synthesizes CT-focused applications. We summarize key architectures, compare reported outcomes using metrics such as Dice coefficient, and discuss their clinical implications. Finally, we highlight gaps including reproducibility, dataset diversity and interpretability, and outline future opportunities in multimodal fusion and real-time deployment. This narrative review provides a concise and modality-focused perspective on the evolving role of deep learning in CT-based liver cancer management.