Accurate prediction of tumor control and toxicities in radiation therapy faces many uncertainties. Besides interpatient variability in the response to radiation, there are also dosimetric uncertainties, that is, differences between the dose displayed in a treatment planning system and the dose actually delivered to the patient. These uncertainties originate from several sources including imperfect knowledge of the patient geometry, approximation in the physics of radiation interaction with tissues, and uncertainties in the biological effectiveness of radiation. Generally, uncertainties are considered in the treatment planning process by applying margins. In intensity-modulated radiotherapy (IMRT), this leads to the planning target volume (PTV) concept. Intensity-modulated proton therapy (IMPT) is widely considered as the future of proton therapy. The treatment planning methods for IMPT and IMRT are similar and based on mathematical optimization techniques for both modalities. However, the PTV concept has fundamental limitations in IMPT. Therefore, researchers have developed robust optimization methods that directly incorporate uncertainties into the IMPT optimization problem. In recent years, vendors of commercial planning systems have started to implement these methods so that robust IMPT planning becomes available in clinical practice. This article summarizes uncertainties in proton therapy and the limitations of the PTV concept to deal with them. Subsequently, robust optimization techniques to overcome these limitations are reviewed.