Organisers said the laws of physics, logic and the predictable would give way to magic and invention.
Thousands of people gathered at the city's castle after a giant peach made its way through the streets, with some ushered back due to sheer numbers.
Dahl was born in Cardiff 100 years ago this month.
People young and old came dressed up as their favourite Dahl characters as more than 35,000 people made their way to the city for the first day of the event.
Thousands of performers are expected to take to the streets for the "surprising events" across the weekend.
However, some people complained on social media about it being too busy and "shambolic" in the city centre. A tightrope walk also had to be cancelled.
A spokeswoman for the event said: "It is fantastic that so many people have come out to enjoy Roald Dahl's City of the Unexpected.
"It is disappointing that due to the sheer volume of the crowd it was necessary to cancel the tightrope walk. All necessary precautions are being taken to ensure crowd safety."
Cardiff Bus said it was "experiencing severe delays across the network due to extremely heavy traffic congestion in and around the city centre".
The city of the unexpected events began in the city centre at 13:00 BST and will run until 21:00 on Saturday.
On Sunday, they will take place between 10:30 and 17:00.
Director Nigel Jamieson said: "For generations, he has been part of our bed times, our childhoods, and the development of our imaginations.
"It is thus fitting that the weekend celebrating his birth in Cardiff will involve one of the most ambitious mobilisations of a city's inhabitants ever attempted, together transforming it into a place that will unlock the child in everyone and create a city of wonder and surprise."
Reality has been turned on its head in Cardiff "as if Roald Dahl is at the helm" to celebrate the author's centenary.