Burning Abyss Decklists
Standard Burning Abyss

Standard Burning Abyss focus on gaining both field and hand advantage through Dante and the other Burning Abyss monsters and using your high amount of Trap cards to clear away any threats that your opponent may have. Kuribandit is used to mill your Burning Abyss monsters to the Graveyard while searching for key Spell or Trap Cards and is extremely powerful during the early game if you can't set up a Dante play.
Barbar is included in this build as it allows for extra burn damage that can be the difference between a win and a loss, especially when used alongside Nightmare Shark. Mistaken Arrest is a very good card choice this format as it stops many of the top decks in their tracks while not hindering Burning Abyss plays. Unlike Mistake, Mistaken Arrest is not a continuous Trap Card, meaning you don't have to worry about not being able to Special Summon from your hand.
Mind Crush is amazing against all of the Tier 1 decks, especially Qliphort, Burning Abyss, and Nekroz.
The Traveler And The Burning Abyss is a very underated card that deserves more consideration. It is essentially a costless Soul Charge that can be used during your opponent's turn and can be brought back by Dante. During your opponent's End Phase, you can activate Fire Lake Of The Burning Abyss to destroy three of your opponent's cards and then use The Traveler And The Burning Abyss to Special Summon those cards back from your Graveyard. If one of the cards sent to the Graveyard was Dante, you can return Fire Lake back to your hand to use again.
Breakthrough Skill was included as it is good against Nekroz and Satellar, as well as being able to negate El Shaddoll Winda, a card that is a real pain for Burning Abyss decks, even when in the Graveyard.
Skill Drain is included as it greatly hinders all the top decks except for Qliphort (a deck that is already almost a free win thanks to Fire Lake). As such, two copies of Acid Golemn are included in the Extra Deck.
Big BA

Big BA focuses on swarming the field with Burning Abyss monsters and spamming the field with Dantes. As such, the deck has a high monster count in order to abuse the Burning Abyss monsters' ability to Special Summon themselves from the hand. It is nearly gauranteed that you will open up at least 2 Burning Abyss Monsters in your opening hand with this deck, meaning that you'll always be able to summon at least one Dante.
This deck works by applying constant pressure to your opponent while gaining insane card and field advantage. The Beginning Of The End usually puts you so far ahead in card advantage that you win after resolving it.
Both Fire Lake and The Traveler And The Burning Abyss are always live because of your large monster count. Having a high monster count allows you to make Virgil's effect live whenever you need him. This deck is extremely fun and powerful.