NoSQL databases were developed to address the limitations of relational databases in handling massive, unstructured datasets. NoSQL databases sacrifice ACID properties like consistency in favor of scalability and availability. The CAP theorem states that only two of consistency, availability, and partition tolerance can be achieved at once. Common NoSQL database types include document stores, key-value stores, column-oriented stores, and graph databases. NoSQL is best suited for large datasets that don't require strict consistency or relational structures.