Biomolecular condensates present in cells can fundamentally affect the aggregation of amyloidogenic proteins and play a role in the regulation of this process. While liquid-liquid phase separation of amyloidogenic proteins by themselves can act as an alternative nucleation pathway, interaction of partly disordered aggregation-prone proteins with preexisting condensates that act as localization centers could be a far more general mechanism of altering their aggregation behavior. Here, we show that so-called host biomolecular condensates can both accelerate and slow down amyloid formation. We study the amyloidogenic protein α-synuclein and two truncated α-synuclein variants in the presence of three types of condensates composed of nonaggregating peptides, RNA, or ATP. Our results demonstrate that condensates can markedly speed up amyloid formation when proteins localize to their interface. However, condensates can also significantly suppress aggregation by sequestering and stabilizing amyloidogenic proteins, thereby providing living cells with a possible protection mechanism against amyloid formation.