Can you help me understand stateful vs stateless routing and how it's used ?
stateful vs stateless routing
The difficult thing about defining this is that everyone means something different without the context of the question. So, I'll throw my hat in too. And hopefully, someone else will as well.
Normally you see this in the context of using Firewalls (i.e. stateful firewalls). So what does this have to do with routing? It is possible to have packets sent through an interface to a destination and that destination gets returned to a different interface than the interface it was sent on. This can occur when you're using multiple firewalls in a clustered situation. You don't know what interface the packet was sent on nor will you know what interface the packet was received as well. This is stateless.
In a stateful firewall setting, the firewall itself tracks the session (the conversation) and knows what interface it was sent and bind that conversation to the interface.