Protein aggregates are the pathogenic hallmarks of many different neurodegenerative diseases and include the accumulation of α-synuclein, the main component of Lewy bodies found in Parkinson's disease. Aggresomes are closely-related, cellular accumulations of misfolded proteins. They develop in a juxtanuclear position, adjacent to the centrosome, the microtubule organizing centre of the cell, and share some protein components. Despite the long-standing observation that aggresomes/Lewy bodies and the centrosome sit side-by-side in the cell, no studies have been done to see whether these protein accumulations impede organelle function. We investigated whether the formation of aggresomes affected key centrosome functions: its ability to organise the microtubule network and to promote cilia formation. We find that when aggresomes are present, neuronal cells are unable to organise their microtubule network. New microtubules are not nucleated and extended, and the cells fail to respond to polarity cues. Since neurons are polarised, ensuring correct localisation of organelles and the effective intracellular transport of neurotransmitter vesicles, loss of centrosome activity could contribute to functional deficits and neuronal cell death in Parkinson's disease. In addition, we provide evidence that many cell types, including dopaminergic neurons, cannot form cilia when aggresomes are present, which would affect their ability to receive extracellular signals.