Liquid-liquid phase separation leads to demixing of proteins from solution and results in a dense, protein-rich phase, which co-exists with a light phase depleted of protein. Recent findings support a model in which phase separation is the biophysical driving force for the formation of membrane-less organelles in the cell, such as stress granules, nucleoli and nuclear speckles. Current open questions are: (i) How is phase separation propensity encoded in the protein sequence, (ii) are dense liquid droplets used as reaction compartments in the cell, and (iii) is physiological phase separation disrupted in disease states? To address them, we study two systems; (a) the RNA-binding protein hnRNPA1, which resides in stress granules and mutations of which are found in ALS patients, and (b) the tumor suppressor Speckle-type POZ protein (SPOP), a substrate adaptor of a ubiquitin ligase, which recruits substrates such as androgen receptor and cMyc. Mutations in SPOP, which interfere with substrate recruitment to the ligase, lead to prostate, breast and other solid tumors. We observe that SPOP mutations also interfere with co-localization of SPOP and its substrates in membraneless organelles. We show that SPOP undergoes phase separation with substrates through multivalent interactions; colocalization in membraneless organelles depends on the same interactions. We show evidence for enzymatic activity in mesoscale assemblies in vitro and in organelles in the cell. This supports a model in which phase separation of this ubiquitin ligase with its substrate is a mechanism for buffering substrate protein levels in the cell and achieving proteostasis. SPOP cancer mutations disrupt phase separation and lead to the accumulation of proto-oncogenic proteins. We will use our work on hnRNPA1 to dissect the molecular grammar that underlies liquid-liquid phase separation through low-complexity domains.