This paper provides a comprehensive review of the existing approaches to ensuring high-precision and reliable GNSS positioning. The purpose of this review is to examine modern approaches to mitigating the main factors affecting GNSS receiver accuracy, including atmospheric delays, ephemeris and clock errors, multipath, and receiver noise, and to highlight the key open challenges in high-precision positioning and error correction. The article presents various error correction techniques and provides their analysis. It presents modern architectural solutions for GNSS receivers aimed at providing high-precision and reliable positioning (conventional, software-defined, multi-frequency and multi-constellation, cloud/edge, integrated GNSS/INS/LiDAR, and integrated GNSS/IoT) and their comparative analysis. The resulting overview will be useful for further research in the field of high-precision navigation.