And now it's time for my personal favorite age of comics - even though I love them all! In the 1970s our good friend the Comics Code Authority started losing power and comics slowly started to immerse themselves in the social issues of the day - mainly feminism and racism. It tackled both of these issues with questionable levels of quality but a great deal of enthusiasm. More to the point, though, these comics combined the fun and hijinks of the earlier ages with actual character development and more serious subject matter. Characters are fleshed out and have interesting relationships and can finally argue with each other.
It was a time of optimism tempered by reality, and fast-growing relationships. Since characters hadn't been fleshed out before this, there's a sharp incline in characters developing dynamics together which is a great deal of fun to read.
DC's modern age is often considered to start with the Green Lantern/Green Arrow hard-traveling-heroes team-up of 1970. In this run of GL's comic, starting with issue #76 Green Lantern and Green Arrow practically take on a different social issue every issue, with nuance and heavy-handed proselytizing going hand-in-hand.
Since these comics look so much more like what we know today, I have less to say about them than the first two ages, but I will say that there are some high quality comics from this era, and if you find yourself annoyed with gratuitous violence and mature content in modern comics yet still want good writing, these may be a great solution.
The Bronze Age also lasts until DC's first universe retcon, Crisis On Infinite Earths so at this point… everything is cannon.
Recommendations
I actually have quite a few comics to recommend from this era! First of all, The Justice League of America, in my opinion, had its hayday in this period. This is during the Justice League's satellite era where their headquarters was the Watchtower in space - objectively their coolest headquarters ever. Unfortunately, the end of the modern era is taken over by Justice League Detroit (and they will have their own chapter, believe me) but for a long time the JLA is going strong here.
Probably the biggest comic to come out of the bronze age is New Teen Titans. Starting in 1980 they do begin in the latter part of the Bronze Age, but they have a long run of amazing bronze-style comics anyway so that's fine. The New Teen Titans are the inspiration for the iconic Teen Titans show with Raven, Starfire, Cyborg and Beast Boy (or Changeling, as he's known in the comic). New Teen Titans revolutionized DC with its incredible character work and nuanced plots interwoven with fantastic art and brilliant theming. It really did push a lot of boundaries, and is probably the most objectively high-quality Titans comic ever, if not one of the best comics of all time. Note that you can enjoy other Titans comics more, and sometimes I do, but I really believe this one is, from a technical perspective, the best they've ever been. It's also the first DC team to begin its existence with a black member - Cyborg.
Batman comics are great in this era as well. With the Silver Age in the past, Batman can get back to his roots as a detective and delve into more serious consequence-laden storytelling. A lot of his chemistry with his supporting cast develops in this era (obviously) and his comics balance character-centric work with thrilling adventure.
The Green Lantern/Green Arrow team up (again, beginning in Green Lantern V2 #76) is also definitely worth a read. Featuring iconic beginnings like the first appearance of John Stewart and Roy Harper's junkie arc this comic addresses a wide variety of social issues without being too depressing or heavy to get through. Also… Green Arrow has never been better than he was in the Bronze Age. Not once. If you like Green Arrow… you have to see him in his heyday - goofy goatee and everything.