Biomolecular condensation arising through phase transitions has emerged as an essential organizational strategy that governs many aspects of cell biology. In particular, the role of phase transitions in the assembly of large, complex ribonucleoprotein (RNP) granules has become appreciated as an important regulator of RNA metabolism. In parallel, genetic, histopathological and cell and molecular studies have provided evidence that disturbance of phase transitions is an important driver of neurological diseases, notably amyotrophic lateral sclerosis (ALS), but most likely also other diseases. Indeed, our growing knowledge of the biophysics underlying biological phase transitions suggests that this process offers a unifying mechanism to explain the numerous and diverse disturbances in RNA metabolism that have been observed in ALS and some related diseases — specifically, that these diseases are driven by disturbances in the material properties of RNP granules. Here, we review the evidence for this hypothesis, emphasizing the reciprocal roles in which disease-related protein and disease-related RNA can lead to disturbances in the material properties of RNP granules and consequent pathogenesis. Additionally, we review evidence that implicates aberrant phase transitions as a contributing factor to a larger set of neurodegenerative diseases, including frontotemporal dementia, certain repeat expansion diseases and Alzheimer disease.