Azure Cosmos DB is a globally distributed, multi-model database service for massively scalable applications with low latency requirements, and has support for NoSQL natively. It has been built by Microsoft Azure from scratch, with global distribution and horizontal scaling in mind. It elastically scales the throughput that is required by these applications and also elastically scales the storage that is required globally. You will only pay for what you need with Azure Cosmos DB.
You can learn more about Azure Cosmos DB at https://azure.microsoft.com/en-us/services/cosmos-db/.
Azure Cosmos DB supports triggers and input and output bindings for Azure Functions.