The citizenship constitutional crisis gripping Canberra groans on today, as the High Court begins its job in judging whether some of the nation's highest-profile politicians can keep their jobs.

Today is the first time five of the declared dual citizenship cases will appear before the highest court in the land.

Who's involved?

Barnaby Joyce — Nationals, Deputy Prime Minister

Matt Canavan — Nationals, former minister

Malcolm Roberts — One Nation, senator

Scott Ludlam — Greens, former senator

Larissa Waters — Greens, former senator

But aren't there others?

Deputy Nationals leader Fiona Nash and South Australian senator Nick Xenophon's cases aren't being heard in this batch, because they announced they were under a citizenship cloud after Parliament finished its business for the week.

They now have to wait until Parliament returns in September to go through the formalities of asking the High Court to decide their fate.

So, what will we learn today?

It's unlikely we'll get much of the substance of each politician's cases revealed in court today. But we may get an insight into how prepared their lawyers are to fight for their political futures.

We'll also learn whether the High Court agrees to the suggestion of Commonwealth solicitor-general Stephen Donaghue QC to deal with the matters "as quickly as possible".

He argued the court should begin its full hearings on September 13 and 14 — just a fortnight from now.

Any attempts by other parties keen to join the cases will also be heard.

Update: The High Court will hold hearings on October 10, 11 to 12. And the court has allowed former MP Tony Windsor to join the challenge against Mr Joyce, who beat Mr Windsor in New England in the last election.

Do we know much about the cases so far?

The solicitor-general's submissions say Barnaby Joyce and Matt Canavan are unlikely to dispute that under the laws of New Zealand and Italy respectively, they are considered citizens of those countries.

That means the argument will go into super-dense debate over how section 44 (1) of Australia's constitution will be interpreted in their cases, given they both maintain they were unwitting dual citizens.

Malcolm Roberts' case will come down to a timeline of events — when did he actually start the process to renounce his dual citizenship?

Scott Ludlam and Larissa Waters have already quit the Senate. Both were dual citizens after being born in New Zealand and Canada.

Could any more pollies be dragged into this?

Well, the Coalition keeps arguing there's a bunch of Labor MPs who haven't proved their citizenship credentials.

Labor says it's rubbish, but the Government could still follow through on its threats to throw them to the mercy of the High Court.

The Opposition is keeping the heat on Liberal MP Ann Sudmalis, despite her claims she was wrongly listed as a British citizen on travel documents from the 1960s.

Will we get any clarity about the constitution?

That's a hard prediction to make. The High Court will eventually have to rule on each of the cases before it.

Whether any the surrounding commentary on interpreting the constitution will help give an overall rule on citizenship remains to be seen.

Stay tuned.