In the anime, it has been stated that "Blue-Eyes" represents power while "Red-Eyes" represents potential.
"Blue-Eyes" Decks aim for a field control strategy, usually by destroying opponent monsters. They can Synchro Summon monsters such as "Azure-Eyes Silver Dragon" to lock down the opponent's field or help Summon stronger monsters and set up a Fusion Summon for a finishing move.
"The White Stone of Legend" needs another effect to discard it and be able to use its Graveyard effect. Whereas both the Monster cards "Master" and "Sage with Eyes of Blue" have effects to Special Summon any "Blue-Eyes" Monster from the Main Deck by either "Shuffles itself from the Graveyard to the Main Deck" ('Spinning to Deck' for short) or Discards itself.
"Dragon's Mirror" is recommended for the Fusion Monster "Neo Blue-Eyes Ultimate Dragon". While it is the only face-up card you control, it can attack up to three times in the same turn by sending other copies of a "Blue-Eyes" Fusion Monster from the Extra Deck to the Graveyard. By sending extra copies of itself to the Graveyard, they will be there to protect any "Blue-Eyes" monster(s) from being targeted by effects by banishing themselves.
You can also use Trap and Spell cards that support LIGHT attribute monsters as virtually every Blue-Eyes monster is a LIGHT monster with a fewexceptions. Spell cards such as "Shine Palace" can support LIGHT monsters beyond Blue-Eyes or Dragons. LIGHT monsters such as "Honest" can easily boost the ATK of your already powerful dragons. Cards such as "Beckoning Light" and "Light of Redemption" can return your destroyed or banished Blue-Eyes monsters to your hand.
Since most Blue-Eyes monsters are LIGHT monsters and Dragons, be cautious if your opponent uses DARK attribute or Fiend type monsters that in general negatively affect LIGHT monsters, and to the worst extent, the anti-LIGHT "Ally of Justice". Light-Imprisoning Mirror can be devastating to a Blue-Eyes deck by negating their effects. Leeching the Light can destroy even your strongest monsters. Also be aware of opponents that use anti Dragon support decks. As this could curtail your entire summoning strategy, relying on your dragons for the bulk of your high ATK monsters can leave you defenseless so high ATK monsters other than Dragons and Blue-Eyes can help. Add to your deck LIGHT monsters that can benefit your dragons. Keep "Lord of Dragons" in your deck to protect against card effects on the field. Your opponent may also try to mill your deck via depriving you of your Blue-Eyes monsters before they can be summoned. Monsters like "Herald of Creation" can return banished Blue-Eyes monsters to your hand. Cards like "Dimension Fusion" can Special Summon Blue-Eyes monsters from the banished zone to the field.