What are the different types of firewalls in networking?

The five types of firewall are:

Packet filtering firewall

Circuit-level gateway

Stateful inspection firewall

Application-level gateway (aka proxy firewall)

Next-generation firewall (NGFW)

Packet filtering firewall

Packet filtering firewalls operate inline at junction points where devices such as routers and switches do their work. However, these firewalls don't route packets, but rather they compare each packet received to a set of established criteria -- such as the allowed IP addresses, packet type, port number and other aspects of the packet protocol headers. Packets that are flagged as troublesome are, generally speaking, unceremoniously dropped -- that is, they are not forwarded and, thus, cease to exist.

Circuit-level gateway

Using another relatively quick way to identify malicious content, circuit-level gateways monitor TCP handshakes and other network protocol session initiation messages across the network as they are established between the local and remote hosts to determine whether the session being initiated is legitimate -- whether the remote system is considered trusted. They don't inspect the packets themselves, however.

Stateful inspection firewall

State-aware devices, on the other hand, not only examine each packet, but also keep track of whether or not that packet is part of an established TCP or other network session. This offers more security than either packet filtering or circuit monitoring alone but exacts a greater toll on network performance.