The Precise Point Positioning (PPP) GNSS data processing technique has developed over the past 15 years to become a standard method for growing categories of positioning and navigation applications. The technique relies on single receiver point positioning combined with precise satellite orbit and clock information and high-fidelity error modelling. This paper uniquely addresses the current accuracy of the technique, and explains the limits of performance, which will be used to define paths for future improvements to the technology. For geodetic purposes, performance typically refers to daily static position accuracy. PPP processing of over 300 IGS stations over one week results in few millimetre positioning rms error in the north and east components and centimetre-level in the vertical (all one sigma values). These results are categorised into quality classes in order to analyse the root causes of the resultant errors: “best”, “worst”, multipath, site displacement effects, satellite availability and geometry, etc. Also of interest in PPP performance is solution convergence period. Static, conventional solutions are slow to converge, with approximately 35 minutes required for 95% of solutions to reach the 20 cm or better horizontal accuracy. From the above analysis, the limitations of PPP and the source of these limitations are isolated, including site displacement modelling, geometric measurement strength, pseudorange noise and multipath, etc. It is argued that new ambiguity resolution and multi-GNSS PPP processing will only partially address these limitations. Improved modelling is required for: site displacement effects, pseudorange noise and multipath, and code and phase biases. As well, more robust undifferenced-phase ambiguity validation and overall stochastic modelling is required.