Three-dimensional human pose estimation (3D HPE) from monocular RGB cameras is a fundamental yet challenging task in computer vision, forming the basis of a wide range of applications such as action recognition, metaverse, self-driving, and healthcare. Recent advances in deep learning have significantly propelled the field, particularly with the incorporation of state-space models (SSMs) and diffusion models. However, systematic reviews that comprehensively cover these emerging techniques remain limited. This survey contributes to the literature by providing the first comprehensive analysis of recent innovative approaches, featuring diffusion models and SSMs within 3D HPE. It categorizes and analyzes various techniques, highlighting their strengths, limitations, and notable innovations. Additionally, it provides a detailed overview of commonly employed datasets and evaluation metrics. Furthermore, this survey offers an in-depth discussion on key challenges, particularly depth ambiguity and occlusion issues arising from single-view setups, thoroughly reviewing effective solutions proposed in recent studies. Finally, current applications and promising avenues for future research are highlighted to guide and inspire ongoing innovation in the area, with emerging trends such as integrating large language models (LLMs) to provide semantic priors and prompt-based supervision for improved 3D pose estimation.