My school has it setup so that all connected devices have an internet facing IP address. That is, they appear to own a subnet: 22.214.171.124/16 (If I recall correctly) where any device can be accessed via that IP address from anywhere.
However, they also have a firewall that blocks certain ports, that all traffic is routed through.
How, in general, is this setup? What kind of hardware, internet service, and software would one use? Is it just something similar to iptables/dnsmasq setup without NAT, using the assigned block as the address space? Is this feasible for a residential connection (ignoring the part where you have to pay fees to ICANN (or whoever) for the IP block)?