SpiceDB is Authzed's open source, Zanzibar-inspired permissions system that operates on a relationship-based approach, allowing for more complex permission resolution. It stores relationships between resources and subjects in its data store, which provides faster performance and consistency compared to other permissions systems. The system can be updated through various methods, including 2PC-like approaches, streaming commits, and asynchronous updates, each with their own advantages and trade-offs. Additionally, SpiceDB allows for more flexible schema designs, enabling applications to not store permissions-related relationships in their relational databases, which can simplify permissions management without compromising performance or consistency.