Precise orbit determination (POD) is the procedure for determining the orbit of a satellite with high accuracy. Compared with global navigation satellite systems (GNSS), the low Earth orbit (LEO) satellites have some different features in space, mainly due to perturbations caused by dynamic forces related to their altitudes. Methods for POD of LEO satellites have been developed over the last decades. Nowadays, postprocessed precise orbits are used in different space applications such as radio occultation, satellite altimetry, and interferometric syntheticaperture radar missions. The advancements in technology decrease the size of LEO satellites and developments in theory increase their orbital accuracy. In recent years, onboard POD has become a hot topic in the navigation and positioning field, which is crucial for, e.g., formation flying of small satellites and GNSS-aided LEO megaconstellations for positioning purposes. This contribution reviews LEO POD methods based on undifferenced GNSS observations in both postmission and real-time data processing. It comprises the quality control step, the models used and their limitations, processing algorithms, and different validation methods. To have a clear insight into the current and the future state of the LEO POD, the most recent developments and important achievements are also discussed.