The Sunday Times will be publishing its annual App List this weekend, featuring the most useful, entertaining and weirdest apps on the planet.

Plus, The Times launches the inaugural Web List, a daily list of the 50 best websites chosen by experts, including celebrities such as pop star Will.i.am, digital guru Martha Lane Fox, property expert Kirsty Allsopp, Tony Blair’s former spin doctor Alastair Campbell, celebrity chef Gordon Ramsay and billionaire entrepreneur Richard Branson.

With the phenomenal rise of smartphones and portable devices, apps have become a way of life for millions of people. Apple users alone downloaded nearly 20 billion apps last year, which is the equivalent of almost three for every person on Earth, and the app boom is set to continue in 2013.

With this in mind, The Sunday Times will be listing and reviewing 500 of the best apps in the world over two weekends starting with Part One this Sunday and culminating with Part Two on Sunday, February 3. The list is broken down over a number of different categories, including arts, business, education, fashion, food and drink, gadgets, news, games, music, shopping, sport, travel and the age-old favourite British subject, weather.

Apps to make the grade this year include: LivingSocial, Great British Chefs, Nigellissima, Malcolm Tucker: the Missing Phone, The Rolling Stones Official App, James May Science Stories and Robots for iPad. Hundreds more have impressed the panel, including both Grand Theft Auto: Vice City and AA Drivesafe, which reward very different styles of driving.

The list also illustrates trends in the app world such as the rise of apps that save you money and the growth of ‘freemium’ apps, which don't charge for the basic app but then sell extra content at a price. Apps that charge more but offer high production values and superb photography or illustrations are also becoming highly sought after.

More than half the apps have never appeared in the list before, showing the rapidly changing market and demand for bigger, better and more sophisticated products.

In addition to the App List, which will appear in The Sunday Times, the inaugural Web List will be published in The Times, providing the essential address book for modern life.

The Web List kicks off with the ‘Top Websites You Can't Live Without’ on Saturday, which includes temporary email generator 10minutemail.com, theswizzle.com that helps people unsubscribe from emails and digitaltheatre.com, which enables theatre to be watched online. Plus, the list provides the best health websites, such as qintervention.org, which gives information about whether someone’s lifestyle choices might lead to a heart attack or stroke and how best to lower the risk.

The Web List continues on Monday with the 50 top websites for fashion and beauty, food and drink on Tuesday, travel on Wednesday, sites that will save you money on Thursday and the 50 best websites for kids and education on Friday.