The mechanisms by which mutations in FUS and other RNA binding proteins cause ALS and FTD remain controversial. We propose a model in which low-complexity (LC) domains of FUS drive its physiologically reversible assembly into membrane-free, liquid droplet and hydrogel-like structures. ALS/FTD mutations in LC or non-LC domains induce further phase transition into poorly soluble fibrillar hydrogels distinct from conventional amyloids. These assemblies are necessary and sufficient for neurotoxicity in a C. elegans model of FUS-dependent neurodegeneration. They trap other ribonucleoprotein (RNP) granule components and disrupt RNP granule function. One consequence is impairment of new protein synthesis by cytoplasmic RNP granules in axon terminals, where RNP granules regulate local RNA metabolism and translation. Nuclear FUS granules may be similarly affected. Inhibiting formation of these fibrillar hydrogel assemblies mitigates neurotoxicity and suggests a potential therapeutic strategy that may also be applicable to ALS/FTD associated with mutations in other RNA binding proteins.