We have been recommending Accompli as an email/contacts/cal solution on iOs and Android for some time now. While not perfect they gave business users a closer approximation of the experience most of our clients have with Microsoft Outlook.
It turns out we were not the only ones to see the similarities as Microsoft has purchased the company that produced Accompli and released a re-branded version named unsurprisingly Outlook.
While this version is virtually if not identical to Accompli it is a separate build and you will want to be using this version as it will be the one receiving new features moving forward. Outlook can downloaded from the links below: