Routers connect computer networks and use routing tables to determine the best path for forwarding packets between networks. They support process and fast switching to process packets, with fast switching being more efficient. Default gateways allow devices to communicate with other networks when a specific route is unknown. Router interfaces must meet criteria like having an IP address to be available. Loopback interfaces allow routers to test themselves without affecting live traffic. Routing tables contain network addresses, interfaces, and metrics to inform forwarding decisions.