White Dwarf is a monthly magazine from Games Workshop which has quite frankly gone to the fucking dogs.
In the beginning, it was just a rubbish magazine that advertised whatever games GW had the rights to publish in the UK, including Dungeons & Dragons (several monsters were actually born out of White Dwarf's "Fiend Factory" article, where fans submitted new monsters - this is where the Slaad came from), Traveler, and RuneQuest. When they produced their own game, Warhammer, it became a primary focus of their magazine. Issue 93 (from 1987) is a big one in /tg/ history, because that's when they announced Warhammer 40,000: Rogue Trader.
The halcyon days were around 1998-99, when 3rd edition 40k was shiny and new and Adrian 'WAAAAAAGH' Wood worked there on a reasonably frequent basis. The general level of grimdark was pretty low and they even included battle reports for the good specialty games as and when they got released, most notably Mordheim and Battlefleet Gothic. Oh and they used to actually put army lists before all of their battle reports, and gave the actual turn-by-turn play. They stopped doing the former because people with calculators were able to backwards engineer army lists from them and thus not buy codices (luckily the internet came along, making buying anything that can be stored in a PDF strictly optional), and they stopped the latter because it meant that their flavor-of-the-month army could get humiliated. Sales fell from here. It was a depressing time for games Workshop.
White Dwarf also used to have a Chapter Approved column with experimental rules and errata. The errata went away when GW realized that they could put errata online and use the saved space for more advertisements, and by the time the experimental rules became actual rules, GW was no longer doing playtesting in public.
Anyway, White Dwarf is alright, but no where near as awesome as it once was. The real point of decline was when it started shilling for the Lord of the Rings game that no-one ever played.
In 2012, GW re-released it. It became a decent magazine, but not worth ten dollars.
In January 2014, it became known that Games Workshop would reinvent White Dwarf again in February. White Dwarf was announced to became a $4, 32-page weekly magazine which would focus on the hobby, featuring, for example, model and book releases, rules updates, and modeling features. Games Workshop would also release a monthly 236-page "Warhammer Visions" magazine at $12, which would also be available for iPad. GW would convert all remaining White Dwarf subscriptions to this "Warhammer Visions" magazine. This magazine would focus on wider hobby news, Citadel model painting examples, various articles to deal with conversions, etc.
Although since 2016 they have gone back to the monthly model. Warhammer Visions died, but now we have a new magazine with batreps, painting tutorials, news, joke segments, and most oddly, FREE SHIT. Issue one came with a fucking SLAUGHTERPRIEST for FREE. The model cost £7 more then the goddammed mag.
In 2019 the magazine got a soft reboot of its contents, being now more like the older times: it contains new short stories for both 40k and Age of Sigmar, the return of Index Astartes with the addition of extra rules to represent the chapters that are not in the Codex (plus multiple variations such as Index Xenos, Index Imperialis and the AoS equivalent The Tome Celestial), more new rules for games (such as new battleplans for both 40k and AoS, new Kill Team armies and models, additional quests for Blackstone Fortress and side game variants of Warhammer Underworlds), more columns and articles about modelling or game strategy and stuff. And absolutely no pages promoting the month's new releases except for the occasional 2-page picture showcasing new stuff or mentions "oh right, this army got a new book and models a few months ago".
Dungeons & Dragons was one of the first game systems to be covered in White Dwarf, back in the days before Warhammer Fantasy. There were quite a few articles, and you can check out the list here: http://wiki.oldhammer.org.uk/v/Dungeons_and_Dragons/White_Dwarf_Index