Cell polarity is crucial for almost every cell in our body to establish distinct structural and functional domains. Polarized cells have an asymmetrical morphology and therefore their proteins need to be asymmetrically distributed to support their function. Subcellular protein distribution is typically achieved by localization peptides within the protein sequence. However, protein delivery to distinct cellular compartments can rely, not only on the transport of the protein itself but also on the transport of the mRNA that is then translated at target sites. This phenomenon is known as local protein synthesis. Local protein synthesis relies on the transport of mRNAs to subcellular domains and their translation to proteins at target sites by the also localized translation machinery. Neurons and glia specially depend upon the accurate subcellular distribution of their proteome to fulfil their polarized functions. In this sense, local protein synthesis has revealed itself as a crucial mechanism that regulates proper protein homeostasis in subcellular compartments. Thus, deregulation of mRNA transport and/or of localized translation can lead to neurological and neurodegenerative diseases. Local translation has been more extensively studied in neurons than in glia. In this review article, we will summarize the state-of-the art research on local protein synthesis in neuronal function and dysfunction, and we will discuss the possibility that local translation in glia and deregulation thereof contributes to neurological and neurodegenerative diseases.