###### Abstract  
GNSS; GPS; GLONASS; Galileo; BDS; precise point positioning; relative positioning; orbit determination; ionosphere sounding; troposphere sounding; geoscience applications; high-rate positioning; GNSS for geodynamics  
In the past two decades, the high-precision Global Positioning System (GPS) has significantly increased the range of geoscience applications and their precision. Currently, it is one of two fully operational Global Navigation Satellite Systems (GNSS), and two more are in the implementation stage. The new European Galileo and Chinese BeiDou Navigation Satellite System (BDS) already provide usable signals, and both GPS and GLONASS are currently undergoing significant modernization, which adds more capacity, more signals, better accuracy, and interoperability, etc. Meanwhile, there has been significant technological development in GNSS equipment (in some cases, even at low-cost), which is now able to collect measurements at much higher rates (up to 100 Hz), thus presenting new possibilities. On the one hand, the new developments in GNSS offer a broad range of new applications for solid and fluid Earth investigations, in both post-processing and real-time; on the other, this results in new problems and challenges in data processing that increase the need for GNSS research. Algorithmic advancements are needed to address the opportunities and challenges in enhancing the accuracy, availability, interoperability, and integrity of high-precision GNSS applications. This special issue aims to provide an overview of the potential of high-precision GNSS for geoscience applications. Besides discussing the current developments in high-precision GNSS constellations, signals and algorithms devoted to Precise Point Positioning (PPP) and Precise Orbit Determination (POD), the special issue focuses on the use of high-precision GNSS in diverse geoscience applications, in terms of geodynamics, seismology, tsunamis, ionosphere, troposphere, etc. An overview of the contributions in this special issue is given in the following paragraphs. Since December 2018, the third generation of BDS (BDS-3) started to provide global-coverage positioning, navigation and timing (PNT) services. The studies conducted on the new BDS satellites and redesigned signals have indicated that the signal in space range error (SISRE) of BDS-3 is superior to that of BDS-2 [1] and the atomic clock has better frequency stability than GPS BLOCK IIF satellites [2]. Among the four open service BDS signals B1I, B1C, B2a and B3I, the ionosphere-free (IF) combination of B1C-B2a was recommended for precise GNSS data processing in regard to the noise amplitude and compatibility with other GNSS. Further research demonstrated that 50%-60% improvements in position accuracy in the east component could be obtained by performing PPP ambiguity resolution (AR) with BDS and Galileo triple-frequency observations, with respect to those achievable with the float solution [3]. Besides the discussion of developments in the GNSS in this special issue, five currently available satellite-based augmentation systems (SBASs) were also evaluated in terms of their orbit, clock and ionosphere corrections [4]. Several studies included in this special issue are dedicated to the advancement of GNSS algorithms and models. [PERSON] et al. [5] proposed a modified least-squares collocation algorithm (LSC) by combining the distance scale factor and adaptive adjustment. The new LSC algorithm better reflects the characteristics of GPS crustal movement and was thus valuable for analysis of regional tectonic dynamics. [PERSON] et al. [6] presented a new cycle slip detection and repair approach for high-dynamic low-earth-orbit (LEO) satellites by making use of second-order time-difference geometry-free (STG) phase combinations. Understanding the characteristics of diverse biases in GNSS data processing is crucial for the refinement of current GNSS algorithms and models. [PERSON] et al.