What is the difference between deep packet inspection and stateful inspection?

Deep packet inspection (DPI) analyzes the data part (and possibly also the header) of a packet as it passes an inspection point, searching for protocol non-compliance, viruses, spam, intrusions, or defined criteria to decide whether the packet may pass or if it needs to be routed to a different destination. Stateful inspection, on the other hand, tracks the state of active connections and determines which network packets to allow through the firewall. While stateful inspection tracks the state of connections (Layer 4 - transport layer), DPI goes further by examining the payload of the packet (Layer 7 - application layer).