BIG-IP Routing Table

I always understand that big-ip will not handle client traffics unless a VS is configured, but when it comes to the routing table it looks like it is a different scenario. Please could someone explain when and in which scenario the big-ip device forwards traffics based on its routing table? what can influence it to handle traffic using its routing table depending on its configuration for VS, SNAT, NAT, etc...?

Thanks in advance for comment.