Imagine these models and associations:

class Deck < ApplicationRecord
  has_many :cards
end

class Card < ApplicationRecord
  belongs_to :deck, optional: true
end

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Now you want to find all Decks without any Card or all Cards without a Deck.

Rails 6.1+

Rails 6.1 introduced a handy method ActiveRecord#missing Show archive.org snapshot to find records without given associations.

Deck.where.missing(:cards)

SELECT "decks".*
FROM "decks"
LEFT OUTER JOIN "cards"
ON "cards"."deck_id" = "decks"."id"
WHERE "cards"."id" IS NULL

Card.where.missing(:deck)

SELECT "cards".*
FROM "cards"
LEFT OUTER JOIN "decks"
ON "decks"."id" = "cards"."deck_id"
WHERE "decks"."id" IS NULL

Older Rails versions

If you don't have Rails 6.1 yet, you can use this not-so-intuitive syntax for the same results:

Deck.left_joins(:cards).where(cards: {id: nil})

SELECT "decks".*
FROM "decks"
LEFT OUTER JOIN "cards"
ON "cards"."deck_id" = "decks"."id"
WHERE "cards"."id" IS NULL

Card.left_joins(:deck).where(decks: {id: nil})

SELECT "cards".*
FROM "cards" 
LEFT OUTER JOIN "decks"
ON "decks"."id" = "cards"."deck_id" 
WHERE "decks"."id" IS NULL