Although no specific date was detailed, it seems that, thanks to a new tie-in between Microsoft and Dropbox, a first party client for the latter will debut on Windows Phone 'in the coming months' - so probably January-ish, 2015. The goal for both companies is to allow editing of documents directly from Dropbox, in much the same way as can be done from OneDrive right now. It seems that one all-singing cloud storage service isn't enough and Microsoft is probably right - more choice is better and Dropbox has significant cross-platform reach and a new (to Microsoft) user base.

From the Microsoft blog post: (my emphases)

Dropbox Inc. and Microsoft Corp. on Tuesday announced a strategic partnership to help people work more effectively. The two industry-leading companies are teaming up to integrate their services for collaboration across Dropbox and Microsoft Office on phones, tablets and the Web.

When you select “edit” while you are viewing your document in Dropbox, the appropriate Office app is offered up for editing. Continue editing, and the apps work together to automatically save your changes back to Dropbox.

....This partnership will enable people at work, home and school to easily collaborate on documents, spreadsheets and presentations. These capabilities will first be available from within the Dropbox and Office apps on tablets and phones, and will soon be accessible via the Web.

Dropbox and Microsoft users can now do the following:

• Access Dropbox from Office apps to get to their files and folders faster.

• Edit Office files directly from Dropbox and sync them across devices.

• Share new or edited files from the Office apps using simple Dropbox sharing functionality.

The functionality will first be included in the next updates to the Office apps for iOS and Android, coming in the next few weeks. The Web integrations between the Dropbox website and Office Online will be available in the first half of 2015. Dropbox will also make its application available on the Windows Phone and Windows tablet platforms in the coming months.

There are Dropbox clients for Windows Phone, e.g. CloudSix and FileBox, but they each have issues and limitations - a first party Dropbox client will be welcomed by all with open arms.

The capabilities mentioned above will be available to all Office users with a Dropbox account, though Dropbox for Business customers will need an Office 365 subscription. 

More information on the tie-in can be found by visiting the Dropbox blog.