Neurodegenerative diseases (NDs) are increasingly positioned as leading causes of global deaths. The accelerated aging of the population and its strong relationship with neurodegeneration forecast these pathologies as a huge global health problem in the upcoming years. In this scenario, there is an urgent need for understanding the basic molecular mechanisms associated with such diseases. A major molecular hallmark of most NDs is the accumulation of insoluble and toxic protein aggregates, known as amyloids, in extracellular or intracellular deposits. Here, we review the current knowledge on how molecular chaperones, and more specifically a ternary protein complex referred to as the human disaggregase, deals with amyloids. This machinery, composed of the constitutive Hsp70 (Hsc70), the class B J-protein DnaJB1 and the nucleotide exchange factor Apg2 (Hsp110), disassembles amyloids of α-synuclein implicated in Parkinson’s disease as well as of other disease-associated proteins such as tau and huntingtin. We highlight recent studies that have led to the dissection of the mechanism used by this chaperone system to perform its disaggregase activity. We also discuss whether this chaperone-mediated disassembly mechanism could be used to solubilize other amyloidogenic substrates. Finally, we evaluate the implications of the chaperone system in amyloid clearance and associated toxicity, which could be critical for the development of new therapies.