This week on Dezeen, Google finally submitted plans for its BIG and Heatherwick-designed London headquarters and chose to honour Zaha Hadid's 2004 Pritzker win with a Google Doodle.

Google's new London HQ is set to feature a huge rooftop garden, a running track and a swimming pool. The tech giant submitted a planning application for the project this week, two years after inviting Bjarke Ingels and Thomas Heatherwick to work on the design.

On Wednesday, the search engine giant dedicated its homepage to Zaha Hadid, with a Google Doodle showing the late architect standing in front of one of her most famous buildings – the Heydar Aliyev Center.

In other news, Anish Kapoor ruffled his neighbours' feathers with plans to add a roof extension to his London studio. Local residents said the expansion will block light and create "prison-like" homes.

And a UK charity has called for architects to find alternative living spaces for Romanian migrant workers who are currently sleeping rough.

In the US, Moscow studio Meganom proposed a skinny supertall tower for Midtown Manhattan and Diller Scofidio + Renfro unveiled the first phase of its MoMA expansion.

OMA revealed plans for its first project in Boston – a development with a huge tree-filled slice cut through its centre.

Elsewhere, Foster + Partners unveiled its latest tree-filled Apple Store – a retail space in Singapore featuring hand-carved stone staircases.

In design news, the world's first paint made from graphene – considered the strongest substance known to science – has launched in the UK.

BMW unveiled a zero-emissions concept scooter that aims to improve urban mobility and Rolls-Royce sold a bespoke car for the price of $13 million.

London Festival of Architecture kicked off this week, so we chose our top picks from the month-long programme's events and exhibitions, including a summer pavilion inspired by John Soane's Dulwich Picture Gallery.

We continued our fashion graduate coverage with a roundup from Parsons' end-of-year show in New York and tapped 15 designers to watch from London's Central St Martins class of 2017.

Popular projects this week included renderings of a loft-style house that go "beyond hyper-realistic", an Indian home with views of the Western Ghats mountains and a domed Greek summer house.