According to some polls, most Spaniards want a referendum to decide whether the country should become a republic.
But the large crowds in Madrid that gathered to greet new King Felipe suggest the royal family has a future.
Many people feel they can relate to him personally.
One man told euronews: “I’ve met him in El Salvador and I think he is a complete gentleman. I think he’s a man that works, he works well and he will do all the best for others.”
“The main challenges for Felipe VI will be the crisis, and the whole issue of the autonomous communities. He has to demonstrate that there’s a parliamentary monarchy in Spain which is very good, much better than a republic,” said one well-wisher.
Some 90 people need treatment for heat exhaustion with the capital experiencing scorching temperatures.
Our correspondent Carlos Marlasca says one of the biggest tests facing Felipe will be whether he can use his symbolic role to spark dialogue between the government and regions like Catalonia, where there’s a growing independence movement.
He says the new king’s first task as head of state won’t be an easy one, as he must try to recover the prestige lost by the Spanish monarchy over recent years.