The goal of radiotherapy is to achieve uniform target coverage while sparing normal tissue. In proton therapy, the same sources of geometric uncertainty are present as in conventional radiotherapy. However, an important and fundamental difference in proton therapy is that protons have a finite range, highly dependent on the electron density of the material they are traversing, resulting in a steep dose gradient at the distal edge of the Bragg peak. Therefore, an accurate knowledge of the sources and magnitudes of the uncertainties affecting the proton range is essential for producing plans which are robust to these uncertainties. This review describes the current knowledge of the geometric uncertainties and discusses their impact on proton dose plans. The need for patient-specific validation is essential and in cases of complex intensity-modulated proton therapy plans the use of a planning target volume (PTV) may fail to ensure coverage of the target. In cases where a PTV cannot be used, other methods of quantifying plan quality have been investigated. A promising option is to incorporate uncertainties directly into the optimisation algorithm. A further development is the inclusion of robustness into a multicriteria optimisation framework, allowing a multi-objective Pareto optimisation function to balance robustness and conformity. The question remains as to whether adaptive therapy can become an integral part of a proton therapy, to allow re-optimisation during the course of a patient's treatment. The challenge of ensuring that plans are robust to range uncertainties in proton therapy remains, although these methods can provide practical solutions.