The Precise Point Positioning (PPP) GPS 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, code and phase observable filtering, and additional 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 of the technology. PPP processing of over 300 International GNSS Service (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, antenna 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 20 minutes required for 95% of solutions to reach a horizontal accuracy of 20 cm or better. From the above analysis, the limitations of PPP and the source of these limitations are isolated, including site displacement modelling, geometric measurement strength, pseudorange multipath and noise, 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 improved stochastic modelling is required for the pseudorange and carrier-phase observables to allow for more realistic position uncertainties.