Project Quadra is a PaaS built on Docker that can run on EC2, OpenStack, or bare metal. It uses GRE tunnels over an overlay network to extend a company's internal network to EC2 instances, but there are some MTU issues to address. BGP is used with Quagga for dynamic routing between the overlay network and EC2 instances, with route filtering and policies configured. Docker networking uses bridges, veth interfaces, and NAT rules to connect containers.