MSDN article on Customizing SharePoint Online using SharePoint Designer 2010:

Why use SharePoint Designer to customize SharePoint Online? In a nutshell, you only have 3 choices:

  • Browser – limited amount of solutions can be created directly through the browser (can’t do things such as powerful workflows, BCS, data views to database data etc.)
  • Visual Studio – within the enterprise, this is a very powerful tool for developers. However, in SharePoint online space, you can only use VS to create sandbox solutions or use the client object model. No farm based solutions
  • SharePoint Designer – This is where the story is Amazing! Almost everything you can do with SharePoint Designer within the enterprise, you can do at SharePoint Online. Powerful workflows, data connections to external systems, management of forms and views for lists and libraries, content types and site columns management… all covered and more. Read the article to see all that can be accomplished with using this product and SharePoint Online