This paper provides a comprehensive survey of recent advancements in Simultaneous Localization and Mapping (SLAM) using Neural Radiance Fields (NeRF) and 3D Gaussian Splatting (3DGS). Over the past two decades, SLAM has evolved from hand-crafted methods to deep learning-based approaches, with NeRF and 3DGS representing a significant shift in the field. The paper highlights the background, evolution, strengths, and limitations of these methods, and serves as a fundamental reference for understanding the dynamic progress and challenges in SLAM. It reviews existing SLAM surveys, discusses radiance field rendering theory, introduces key datasets and benchmarks, and describes main evaluation metrics. The core of the paper focuses on key NeRF and 3DGS-inspired SLAM techniques and their structured taxonomy. It presents quantitative results evaluating SLAM frameworks in tracking, mapping, rendering, and performance analysis across diverse scenarios. The paper also discusses limitations, future research directions, and summarizes the survey comprehensively. The paper reviews various SLAM systems, including RGB-D, RGB, and LiDAR-based approaches, and highlights their key features, input modalities, mapping properties, additional outputs, tracking properties, advanced design strategies, and use of additional priors. The paper also discusses evaluation metrics for SLAM systems, including mapping, tracking, view synthesis, and semantic segmentation. The paper concludes that NeRF and 3DGS have significantly reshaped SLAM, offering continuous surface modeling, reduced memory requirements, improved noise handling, and enhanced hole filling and scene inpainting capabilities. However, each technique has its own strengths and limitations, and the field is constantly evolving, requiring ongoing research and innovation to make further progress.This paper provides a comprehensive survey of recent advancements in Simultaneous Localization and Mapping (SLAM) using Neural Radiance Fields (NeRF) and 3D Gaussian Splatting (3DGS). Over the past two decades, SLAM has evolved from hand-crafted methods to deep learning-based approaches, with NeRF and 3DGS representing a significant shift in the field. The paper highlights the background, evolution, strengths, and limitations of these methods, and serves as a fundamental reference for understanding the dynamic progress and challenges in SLAM. It reviews existing SLAM surveys, discusses radiance field rendering theory, introduces key datasets and benchmarks, and describes main evaluation metrics. The core of the paper focuses on key NeRF and 3DGS-inspired SLAM techniques and their structured taxonomy. It presents quantitative results evaluating SLAM frameworks in tracking, mapping, rendering, and performance analysis across diverse scenarios. The paper also discusses limitations, future research directions, and summarizes the survey comprehensively. The paper reviews various SLAM systems, including RGB-D, RGB, and LiDAR-based approaches, and highlights their key features, input modalities, mapping properties, additional outputs, tracking properties, advanced design strategies, and use of additional priors. The paper also discusses evaluation metrics for SLAM systems, including mapping, tracking, view synthesis, and semantic segmentation. The paper concludes that NeRF and 3DGS have significantly reshaped SLAM, offering continuous surface modeling, reduced memory requirements, improved noise handling, and enhanced hole filling and scene inpainting capabilities. However, each technique has its own strengths and limitations, and the field is constantly evolving, requiring ongoing research and innovation to make further progress.