Drayden and Iris are the Gym Leaders of the Opelucid City Gym. They both use Dragon-types.
In Pokémon Black/White, their teams consist of: Level 41 Fraxure, with Dragon Dance, Dragon Rage, Assurance and Dragon Tail, Level 41 Druddigon with Revenge, Chip Away, Night Slash and Dragon Tail and finally Level 43 Haxorus with Dragon Dance, Slash, Assurance and Dragon Tail. Drayden's (Black) Druddigon has Rough Skin as its Ability, while Iris' (White) has Sheer Force instead. His team is all male, hers all female.
Tips for beating Drayden/Iris:[]
Knock out both Fraxure and Haxorus as quickly as possible: Both of these olive blade wielders have Dragon Dance, and it should be obvious why that makes the base 147 Attack / 97 Speed Haxorus a nightmare in a region where the fastest Pokémon that are easy to obtain are Serperior and Swoobat, which are both outsped at +1. Bring a Pokémon with an Ice move and hope that you OHKO it or abuse Dragon Tail's low priority if needed to finish the job should it survive a hit. Fraxure's less threatening due to its much lower bulk, although it will carve a hole through anything that attempts to fight it after a few dances.
Be mindful of the genders: This again applies to the Fraxure and Haxorus, as both will always have Rivalry, which makes fighting Drayden with the starters, elemental monkeys and Sawk/Throh risky as the already high Attack that the Axew line possesses will likely receive a power boost due to the trios being skewed towards male gender ratios and the later duo always being male. For Iris, just be careful of any female Pokémon you send against her dragons.
Intimidate and status inflicters are still your friends: Given that all three of their Pokémon have all physical movesets with high Attack stats to work with, being able to neuter their offensive prowess -- even if only temporarily in Fraxure's and Haxorus' case -- is a valuable ability to have. If you have something that can paralyse or burn Haxorus, you've already massively reduced the threat it poses; as per normal, all three are relatively easy targets when asleep.
Try to avoid physical contact with Druddigon (Black only): Residual damage is something you do not want to be taking against a powerful bulky Dragon that has Revenge to murder the most common answers for it (Ice and Steel-types). It has very good coverage (Dragon + Fighting + Dark) and will hit reasonably hard against pretty much anything; and, unlike its teammates, it can take a few hits and actually get good use out of Dragon Tail. The last thing you need is to knock it out at low health and then be reminded of its Ability by a dead team member.
Good Pokémon to use:[]
Beartic/Vanilluxe/Cryogonal: The first two are able to weather the force behind the Dragons' offensive while shutting them down with Icicle Crash or Ice Beam, respectively. Just be careful of Druddigon's Revenge, which will do a ton of damage if you fail to OHKO. Crygonal can outrun all three, but its paper-thin Defense means that unless you are massively overleveled to point of being guaranteed to OHKO all three, Druddigon and possibly Haxorus will survive Ice Beam and shatter you.
Anything that can boost its Defense/weaken the attacking power of the Dragons: The main threat of their teams is the Dragon Dance Haxorus, but Pokémon like Serperior can boost their defenses alongside the monster, allowing them to keep up with its boosts. Serperior gets special mention due to Coil boosting its Attack as well, meaning that Return will deal a good amount of damage at +1/+2 (just be wary of Rivalry). Also notable is Amoonguss, which is able to negate the buffs with Clear Smog and use Spore to cripple their teams.
Haxorus: If you have one of these, it will be five levels higher than the opposition. Spam Dragon Claw and watch everything crumble beneath your Dragon's wrath. You can also set up against Fraxure if needed, just to obliterate all who oppose you. However, if your Haxorus has a Speed-lowering Nature, it'll be very risky to pit it against Drayden's/Iris' Haxorus.