In February 2014, the Supreme Court of Mexico, citing US scholarship and case law, held that punitive damages had to be awarded to a tort plaintiff as part of the indemnity afforded by Mexican law under the heading of moral damages (daños morales). Before this landmark decision, nothing similar to punitive damages existed in the Mexican legal system. In the context of arbitral proceedings, this new interpretation of moral damages gives rise to two questions at the core of the international discussion on punitive damages and arbitration. The first has regard to the power of arbitral tribunals with seat in Mexico to award punitive relief when the applicable substantive law, including Mexican law, contemplates it. The second is the possibility of enforcing foreign-based law punitive damages awards in Mexico. Despite the early stage and still incipient discussion regarding the true nature and application of punitive damages in Mexico, the author forecasts that, while they may be an available relief in arbitration proceedings in Mexico, this decision is a rare exception and their quantum limited. In addition, Anglo-American law based punitive damages awards may still find a public policy obstacle for their enforcement or grounds for their nullity in Mexico.