There is a cautious welcome for the winner of Iran's presidential election, the reformist-backed candidate Hassan Rouhani.
But it would be wrong to get carried away, the Times warns. Mr Rouhani is not a reformist himself, the paper says.
"For most of his career, he has been at the centre of Iran's conservative clerical establishment," it adds.
"In any case, the ultimate say on key issues lies with the Supreme Leader."
The Independent points out that we do not know yet what he would do with Iran's nuclear programme.
But the presidency does offer a "chance for the West to reset relations with Iran", it says.
According to the Guardian, foreign politicians and officials at two G20 summits in London in 2009 had their computers monitored and phone calls intercepted on the instructions of the British government.
The paper says some delegates were tricked into using internet cafes which had been set up to read their email traffic.
The G20 spying appears to have been organised for the purpose of securing an advantage in meetings, it adds.
The paper says the evidence is contained in documents seen by the paper that have been revealed by the American whistleblower, Edward Snowden.
The government is meeting internet service providers to discuss concerns about online porn and images of child abuse - and the Daily Mail says this time they must match rhetoric with action.
While ministers have dithered, lives have been destroyed by internet filth, it says.
In the Sun's view, any parent of young children knows that internet companies are still not doing enough to ban child abuse websites.
When they arrive for the meeting they should expect straight talk - and the only acceptable response from them is action, the paper adds.
The Mirror's main story says police are looking into an incident involving television chef Nigella Lawson and her husband Charles Saatchi.
A picture showing him apparently with his hand on her throat features in most papers. The Telegraph says she was apparently assaulted during a row outside a restaurant.
Finally, wine lovers will be interested to hear about the invention of a cork that does not need a corkscrew.
According to the Times, it is called the Helix cork - and it has a thread finish that drinkers can twist in and out of the neck of the bottle.
Its creators, a Portuguese cork manufacturer and American bottle maker, hope it will revive the popularity of corks which they believe drinkers have always preferred.
The Mail says the companies claim that wine stored with a Helix cork tastes no different to a classic bottle, and important factors used by critics to judge wine - such as colour and smell - are also unaffected.