Positron emission tomography (PET) images are degraded by a phenomenon known as the partial volume effect (PVE). Approaches have been developed to reduce PVEs, typically through the utilisation of structural information provided by other imaging modalities such as MRI or CT. These methods, known as partial volume correction (PVC) techniques, reduce PVEs by compensating for the effects of the scanner resolution, thereby improving the quantitative accuracy. The PETPVC toolbox described in this paper comprises a suite of methods, both classic and more recent approaches, for the purposes of applying PVC to PET data. Eight core PVC techniques are available. These core methods can be combined to create a total of 22 different PVC techniques. Simulated brain PET data are used to demonstrate the utility of toolbox in idealised conditions, the effects of applying PVC with mismatched point-spread function (PSF) estimates and the potential of novel hybrid PVC methods to improve the quantification of lesions. All anatomy-based PVC techniques achieve complete recovery of the PET signal in cortical grey matter (GM) when performed in idealised conditions. Applying deconvolution-based approaches results in incomplete recovery due to premature termination of the iterative process. PVC techniques are sensitive to PSF mismatch, causing a bias of up to 16.7% in GM recovery when overestimating the PSF by 3 mm. The recovery of both GM and a simulated lesion was improved by combining two PVC techniques together. The PETPVC toolbox has been written in C++, supports Windows, Mac and Linux operating systems, is open-source and publicly available.