The National Institute of Standards and Technology (NIST) 800-10 has divided firewalls into three basic types:
Packet Filters - check incoming and outgoing traffic by creating a checkpoint at a traffic router or switch.
Stateful Inspection - combines packet inspection technology and TCP handshake verification for enhanced protection.
Proxys (or Application Level Gateways or Firewalls) - operate at the application layer and works by establishing a connection to the traffic source and inspecting the incoming data packet.
There are two more types of firewalls that are currently available:
Circuit-Level Gateways - verify the Transmission Control Protocol (TCP) handshake which is designed to check that the packet session is legitimate.
Next-Gen Firewalls - include architectures such as deep-packet inspection, TCP handshake checks and surface level packet inspection.