Microsoft Planner is one of the Office 365 modules that you may not be that familiar with. It's not really a project planner in the grand sense of the word (unlike Project Studio), but instead "Planner enables users and teams to create plans, assemble and assign tasks, share files, communicate and collaborate with other users, and receive progress updates via various means on the Office 365 platform". It was launched last year and is only now coming out on phones, starting with the iPhone (what with the USA being iPhone mad, yada yada). However, there's evidence to suggest that Android and Windows 10 Mobile may not be far behind.
Microsoft Planner on the iPhone is here in the iOS App Store, in case you have an iPhone or iPad that youd like to try it all out on.
Having a dedicated phone application is a lot cleaner and faster than having to go via a web browser, which was the case (and still is, for the time being, on Windows 10 Mobile).
In terms of a future Windows 10 UWP version (so that would be mobile compatible, etc.), I'm heartened by this graphic on the main Planner web page:
Yes, I know it's something of a mock-up, but 'Microsoft' branding on the phone outline and the Windows-esque controls (never mind that they're 8.1-ish!) indicates some degree of inclusion of Windows 10 Mobile too. Plus Android is a shoe-in, of course, in time.