good question. require? nothing - canister filer aside:
sumps serves several purposes, primarily serving to hide equipment keeping it out of sight of the display tank (like a protein skimmer) and serving as a refugium - a safe place for life to grow without predatation of the tank critter (or vice versa), such as macro algae.
The better question is what do I need for my tank that i don't want to put in my display tank. This usually requires thought into what type of filtration do you want. A nano tank with live rock may not need any, relying on water changes only. Protein skimmers remove organics prior to them breaking down. Carbon reactors take out stuff that the protein skimmers don't. They are often combined with gfo to remove PO4. a refugium (typically macro algae, and/or live rock and/or sand ) uptake NO3 and PO4.
A sump is usually where you keep your ATO and dosing pumps if you automate those functions. Placing (a) heater(s) in the sump keeps them out of sight
filter socks catch debris/detritus before it breaks down (but to be effective should be changed twice a week)
Algae Turf Scrubbers (ATS) are another form if filtration often housed in a sump.
Is that enough to get your head spinning?
do a quick search of the Berlin Method to familiarize yourself with the basic filtration concept. Most tanks use some variation of this. I subscribe to the notion of don't add anything unless you need to address something, with one exception. I would not have a coral tank without running activated carbon. Corals engage in chemical warfare and some of these can melt and release their toxins throughout the tank. I view carbon as an insurance policy and not an actual necessity.