You can take a free carry-on bag measuring 56 x 25 x 45 cm on every flight, regardless of fare. An extra laptop or handbag is a matter of course.
Checked baggage up to 23 kg is free on selected long-haul flights only. A recent trend has forced Iberia to charge €45 per way for checked baggage on long-haul flights, even on the lowest fares.
If you want to travel with larger luggage even on flights within Europe, you have to either buy a more expensive ticket or pay an extra €15 per piece per direction.
For an animal up to 8 kg (carried in the cabin), the fee is €25, and an animal carried in the luggage compartment costs €120. Fees to the USA are roughly 2.5 times higher.