What	Rails version	Within `before_*`	Within `after_*`
Cancel later callbacks	Rails 1-4	`return false`	`return false`
Cancel later callbacks	Rails 5+	`throw :abort`	`throw :abort`
Rollback the transaction	Rails 1-4	`return false`	`raise ActiveRecord::Rollback`
Rollback the transaction	Rails 5+	`throw :abort`	`raise ActiveRecord::Rollback`

Take care that your callbacks don't accidentally return false, since that cancels the chain in Rails 1-4 (returning nil is fine, though). Since in Ruby the last expression of a method becomes its return value automatically, this can happen accidentally:

before_save :callback

def callback
  call_to_method_that_happens_to_return_false
end

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When a callback raises an error

Exceptions raised in callbacks always rollback the transaction, but only exceptions that are not ActiveRecord::Rollback will bubble up to the caller.

Cancelling the ActiveRecord callback chain

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When a callback raises an error

Further reading