The growing demand for radiological services, amplified by a shortage of qualified radiologists, has resulted in significant challenges in managing the increasing workload while ensuring the accuracy and timeliness of radiological reports. To address these issues, recent advancements in artificial intelligence (AI), particularly in transformer models, vision-language models (VLMs), and Large Language Models (LLMs), have emerged as promising solutions for radiology report generation (RRG). These systems aim to make diagnosis faster, reduce the workload for radiologists by handling routine tasks, and help generate high-quality, consistent reports that support better clinical decision-making. This comprehensive study covers RRG developments from 2021 to 2025, focusing on emerging transformer-based and VLMs, highlighting the key methods, architectures, and techniques employed. We examine the datasets currently available for RRG applications and the evaluation metrics commonly used to assess model performance. In addition, the study analyzes the performance of the leading models in the field, identifying the top performers and offering insights into their strengths and limitations. Finally, this study proposes new directions for future research, emphasizing potential improvements to existing systems and exploring new avenues for advancing the capabilities of AI in radiology report generation.