Spain's main carriers set their own pet policies rather than following one national standard, so it's worth checking the specific airline before booking. Iberia's official pet policy caps cabin travel at 8kg including the carrier, with a carrier no larger than 45 x 35 x 25cm, and charges a fee that varies by route — around €35 within Spain, €50 to Europe, North Africa and the Middle East, and €150 on its longer-haul destinations, paid at the airport per direction. Hold travel is also available on Iberia, subject to aircraft-specific carrier limits and its own separate fee scale.
Vueling runs a notably different model: pets fly in the main cabin only, in a carrier up to 8kg combined weight and no larger than 45 x 39 x 21cm, for a fee of €40 each way domestically and €50 internationally — and the airline states directly that it doesn't offer checked baggage or hold travel for live animals at all. That makes Vueling a workable option only for a small pet that fits the cabin limit, with no larger-dog alternative on that airline.
Across both carriers, brachycephalic (flat-faced) breeds face extra restriction in the hold, and neither airline carries pets to or from the UK or Ireland on international routes — a detail worth checking if your trip to Spain is a connecting leg from there. As with any airline, cabin pet spots are limited per flight, so book your pet's spot when you book your own ticket rather than after.