This report presents a comprehensive review and comparison of various imaging modalities used in the detection of primary hepatic malignancy, specifically hepatocellular carcinoma (HCC), in patients who have undergone liver transplantation. The study analyzes the diagnostic performance of Computed Tomography (CT), Magnetic Resonance Imaging (MRI), Ultrasonography (US), and Positron Emission Tomography (PET) in identifying and staging HCC. The report delves into the advantages and limitations of each technique, considering factors such as image resolution, invasiveness, cost, and radiation exposure. It synthesizes findings from multiple research articles and clinical guidelines, including those from the European Journal of Radiology and the Journal of Hepatology, to provide a detailed overview of the current best practices in HCC imaging. The analysis covers aspects such as the role of contrast-enhanced imaging, the use of radioactive tracers in PET, and the impact of these techniques on patient management and treatment allocation. Ultimately, the report aims to provide insights into the most effective detection strategies for HCC in the context of liver transplantation, contributing to improved patient outcomes.