The crucial issue is whether the phones, which use GPS technology and connect to external servers to carry out calculations, are taximeters, which are prohibited in private hire vehicles in London.
The two-day case is being heard by Mr Justice Ouseley with the main trade bodies - the Licensed Taxi Drivers' Association and Licensed Private Hire Car Association - joining in the application for judicial review.
TfL has stated that, on balance, it believes smartphones are not taximeters but concedes there are clearly arguments to the contrary and there is a significant public interest in resolving the matter definitively.
Leon Daniels, TfL's managing director of surface transport, referred to the technological changes now taking place and said: "London is one of the world's great technology centres – and we celebrate that.
"In order to move with these changes, whilst still ensuring the safest and best possible journeys for passengers, it is in everyone's interest to bring legal clarity to the issue of taximeters and to review the current regulations that were written well before smartphones were invented."
Black cab drivers have demonstrated in the capital against TfL's handling of regulation for private hire car companies, in particular Uber, and suggested that the ride-sharing taxi app puts public safety at risk.
Uber itself has hit out against proposals to tighten private hire regulation following TfL's launching of a consultation on a series of measures that would affect minicab drivers in the capital.
They include the introduction of an interval of at least five minutes between a booking and the start of a journey, to allow drivers to plan an appropriate route.
Other proposals involve a requirement for drivers to pass an English language test and a map reading assessment, while firms could have to operate a fixed landline telephone and accept bookings up to seven days in advance.
Uber is urging its customers to sign a petition as it warned the plans "will mean an end to the Uber you know and love today".
Government figures show the number of minicabs in the capital has risen by over a quarter (26%) in the past two years, to 62,800.
London mayor Boris Johnson said he is seeking legislation to give TfL the power to cap the number of licensed minicab drivers.
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