Deadly attacks on Saudi Arabian airports in recent days, plunging air travel across the kingdom into chaos, have marked a dangerous new escalation in the country's long-running conflict with Yemen's Houthi rebels.

And as the smoke had barely cleared from an attack on Riyadh airport that killed 13 people the Iranian-backed group issued an ominous warning: the worst is yet to come.

It is another concerning development in a region already grappling with a grinding stalemate in another war, as talks between the US and Iran go nowhere fast.

The situation also presents a challenge for Saudi Arabia, which has spent years trying to assert its dominance in the region and reinvent its image as a haven for investment and opportunity.

Experts say the attacks have highlighted gaps in the Saudis' defences, with some reports suggesting the country is running low on defensive missiles.

Resolving the crisis might be impossible without a deal to end the broader war between Washington and Tehran — and even then, it is not entirely clear-cut.

"The Houthis, in some sense, have been and remain a proxy, a partner of the Iranians, but they're increasingly independent-minded," former US ambassador to Saudi Arabia Michael Ratney told the ABC.

"In a strange way, that's especially dangerous — the idea that the Houthis might no longer be an Iranian proxy means that they can no longer be influenced simply by cutting a deal with Iran.

"And they're highly ideological, highly belligerent towards the Saudi monarchy and [have] become this huge problem in their own right."

Why are the Houthis and Saudi Arabia fighting?

In 2015 the Saudis intervened in the civil war in Yemen, backing the country's internationally recognised government against the Houthis.

The paramilitary group — designated a terrorist organisation by several countries, including Australia — had been demanding greater autonomy for the areas it controlled, and wanted to oust the Yemeni government.

Since the Houthis took control of the capital, Sanaa, as well as northern and western Yemen, Saudi Arabia has been supporting the government in the south.

Part of the Saudis' support included a blockade of Yemen, contributing to the humanitarian crisis inside the country.

The conflict raged until a ceasefire was brokered between the Saudi-led coalition and the Houthis, enforced from March 2022.

Fast forward to the middle of this year when the truce was shattered.

The Saudis launched air strikes on Yemen's international airport in Sanaa in July, targeting the runway in a bid to stop an Iranian plane from landing. The Houthis, in response, launched missiles at a regional Saudi airport.

These were the opening salvos in what has since become a major escalation.

The Houthis also announced a maritime blockade of Saudi Arabia in the Red Sea, threatening to effectively block the narrow Bab el Mandeb Strait through which the Saudis dispatch millions and millions of barrels of oil to global markets.

The group said the blockade was in response to Saudi Arabia's "oppressive siege" on Yemen over the past 12 years.

Airport attacks mark 'difficult' escalation

While the Houthis have been attacking the Saudis for months now, the situation has changed.

In recent days, multiple strikes have hit King Khalid International Airport in the capital Riyadh — including one attack on Saturday as the airport was full of pilgrims travelling to visit Muslim holy sites in Mecca and Medina.

The strike killed 13 people and injured more than 300, making it one of the largest mass casualty attacks in recent Saudi history, said Thomas Juneau, a professor from the University of Ottawa's Graduate School of Public and International Affairs.

"We have seen the Houthis over the years targeting with missiles or drones critical infrastructure in Saudi Arabia, oil infrastructure, airports, the Formula One race a few years ago," he told ABC Radio National.

"But what we are seeing … is an escalation."

The situation has tested Saudi air defences, with reporting in media outlets including the Wall Street Journal suggesting the country may now be running low on interceptor missiles.

"[The Houthis] can fire like tens of drones and missiles and at least one of them … will cause the damage," Maysaa Shuja Al-Deen, senior researcher at the Sana'a Center, told the ABC.

"They don't aim to destroy the whole facility. It's only to harm it, to cause the damage is enough for them.

"It's very difficult with this kind of weapons to assure or to guarantee that you have a defence system that guarantees 100 per cent protection."

Mr Ratney said the Saudis would be looking for any help they could get from the US, even if predicting how US President Donald Trump might respond to Crown Prince Mohammed bin Salman's requests for assistance was difficult.

"The Saudis have considerable air defences, including Patriot missile batteries — they have probably more than most countries in the world at this point, but it's obviously not enough," he said.

"It's a huge country and, when you think about it, they're going to prioritise their energy infrastructure, particularly in the east.

"And I think in some ways, they didn't totally factor in the potential for the Houthis to start targeting areas like civilian airports."

Why Saudi-Houthi negotiations will be 'difficult'

Ms Shuja Al-Deen said the Houthis currently have the upper hand in the conflict, complicating any deal to end it.

"It's very difficult to sit at the negotiation table and assume that everyone will give all the concessions for the Houthis based on this military situation — and now also because the Yemeni war is now overlapping with the regional war," she said.

Professor Juneau said the objective behind the Houthis' escalation was to "continue to build their leverage relative to Saudi Arabia".

"One day, I have no idea when, and not in the short term, but one day there will be negotiations for some kind of political resolution between Saudi Arabia and the Houthis," he said.

Mr Ratney said it was an issue that needed greater international focus, as it went "beyond Saudi Arabia".

"And sooner or later, I think the West, the Middle East, are going to have to figure out a way to deal with it," he said.

"I think from the Saudi and broader Gulf perspective, that's uncertainty that they don't need right now.

"They just want this war de-escalated, and they want to be able to get back to, in the case of Saudi Arabia, their whole economic transformation initiative, investment, tourism, everything that they've been working towards."