Many biomolecular condensates appear to form via spontaneous or driven processes that have the hallmarks of intracellular phase transitions. This suggests that a common underlying physical framework might govern the formation of functionally and compositionally unrelated biomolecular condensates. In this review, we summarize recent work that leverages a stickers-and-spacers framework adapted from the field of associative polymers for understanding how multivalent protein and RNA molecules drive phase transitions that give rise to biomolecular condensates. We discuss how the valence of stickers impacts the driving forces for condensate formation and elaborate on how stickers can be distinguished from spacers in different contexts. We touch on the impact of sticker- and spacer-mediated interactions on the rheological properties of condensates and show how the model can be mapped to known drivers of different types of biomolecular condensates.