The increasing demand for medical imaging has surpassed the capacity of available radiologists, leading to diagnostic delays and potential misdiagnoses. Artificial intelligence (AI) techniques, particularly in automatic medical report generation (AMRG), offer a promising solution to this dilemma. This review comprehensively examines AMRG methods from 2021 to 2024. It (i) presents solutions to primary challenges in this field, (ii) explores AMRG applications across various imaging modalities, (iii) introduces publicly available datasets, (iv) outlines evaluation metrics, (v) identifies techniques that significantly enhance model performance, and (vi) discusses unresolved issues and potential future research directions. This paper aims to provide a comprehensive understanding of the existing literature and inspire valuable future research.