Similar to other polypeptides and electrolytes, proteins undergo phase transitions, obeying physicochemical laws. They can undergo liquid-to-gel and liquid-to-liquid phase transitions. Intrinsically disordered proteins are particularly susceptible to phase separation. After a general introduction, the principles of in vitro studies of protein folding, aggregation, and condensation are described. Numerous recent and older studies have confirmed that the process of liquid-liquid phase separation (LLPS) leads to various condensed bodies in cells, which is one way cells manage stress. We review what is known about protein aggregation and condensation in the cell, notwithstanding the protective and pathological roles of protein aggregates. This includes membrane-less organelles and cytotoxicity of the prefibrillar oligomers of amyloid-forming proteins. We then describe and evaluate bioinformatic (in silico) methods for predicting protein aggregation-prone regions of proteins that form amyloids, prions, and condensates.