A traditional firewall leverages stateful inspection. This means that it looks principally at network headers, including states, ports, and protocols. However, newer systems have started to integrate features of other, payload-based information, which is why it is considered here. 

A Unified Threat Management (UTM) firewall combines stateful inspection with intrusion prevention and antivirus.

Next-generation firewalls (NGFW) additionally integrate a system for upgrades, typically also leveraging the cloud for new virus and malware definitions. Application awareness (as described here) can also be added to provide more granular control.

The threat-focused NGFW is one of the newer advancements, as they can not only detect and block threats in progress but can also make changes to the policies on the inbound interface to prevent similar attacks in the future.