Convection-enhanced delivery (CED) describes a direct method of drug delivery to the brain through intraparenchymal microcatheters. By establishing a pressure gradient at the tip of the infusion catheter in order to exploit bulk flow through the interstitial spaces of the brain, CED offers a number of advantages over conventional drug delivery methods - bypass of the blood-brain barrier, targeted distribution through large brain volumes and minimisation of systemic side-effects. Despite showing early promise, CED is yet to fulfil its potential as a mainstream strategy for the treatment of neurological disease. Substantial research effort has been dedicated to optimising the technology for CED and identifying the parameters which govern successful drug distribution. It seems likely that successful clinical translation of CED will depend on suitable catheter technology being used in combination with drugs with optimal physicochemical characteristics, and on neuropathological analysis in appropriate pre-clinical models. In this review we consider the factors most likely to influence the success or failure of CED, and review its application to the treatment of high-grade glioma, Parkinson's disease (PD) and Alzheimer's disease (AD).