Research in the past one and a half decade has demonstrated that not all proteins function as folded structures. Intrinsically disordered proteins (IDPs) perform critical functions, especially for the regulation of cellular processes in higher organisms. Quite remarkably, it has been discovered recently that some IDPs function not only as individual molecules, but also collectively by undergoing liquid-liquid phase separation in the cell. The resulting high-IDP phase forms a major component of membraneless organelles that, by creating their own IDP-rich compartments, enables critical biological functions. Malfunctioning of some of these phase separation processes can lead to diseases. To gain physical insight into this fascinating phenomenon, I will discuss recent theoretical developments to elucidate how IDP phase separation is governed by their amino acid sequences.