In this review article, we highlight the impact of models incorporating flavour symmetries on charged lepton flavour violating (LFV) processes. Flavour symmetries provide a natural approach to explain the peculiar mass hierarchies and mixing patterns of the Standard Model fermions. New sources of LFV are generally present in new physics beyond the Standard Model, and flavour symmetries can make distinctive predictions for LFV observables. Their discovery can provide crucial information to distinguish flavour symmetries and new physics scenarios in general. Because of their high sensitivity, we will focus on searches for low-energy LFV processes such as μ → e γ or μ-e conversion in nuclei but we will also highlight the potential impact of LFV processes at the LHC. If new physics occurs at a scale accessible by the LHC, the flavour operators they induce could potentially be probed in high detail.