It should be possible to synchronize Outlook with Apple Contacts, including iCloud contacts and to import Mails and folders from Apple Mail.

Amazon Cloud, LiveDrive, Adobe Creative,Mega Cloud, DS Cloud, Egnyte, Sharefile, Sharesync, WD Cloud, OwnCloud, WebDAV, Yandex, Sugarsync, SOONR, Teamwork Projects, Sync.com, Baidu cloud etc..

Create, Edit and Delete Folders.
Auto-collapse folders in the side bar when the list is too long.
Arrange order of folders

1) Allow for categorizing email in Outlook on iOS.
2) Show categories assigned in desktop client.
3) Allow sorting by category in Outlook on iOS.

It would be great to have my notes in my Exchange account can sync with my Outlook.

It would sure be nice to have the option to change the sort order in which the emails appear within the threads. I, for example, would like the most recent email to show up at the top of the list. Currently the most recent email is showing at the bottom.

Ability to customize the sounds and volume for notification alerts, just like Apple Mail.

Please expand keyboard support on iPads, this will make the app much easier to use on the iPad Pro

For example
Cmd-S to search for mail
Delete key to delete messages

Set dates and times when you will not receive notifications.

Delete PDFs, jpegs or any other type of file in files section

Also, delete entire file folders

The ability to see rules and create rules for an entire domain. I frequently have emails from users within my domain that make it into the non-focused inbox.

I would like a way of forcing all emails from my users into my focused inbox.

It would be helpful to see the unread message count for each separate account on the accounts menu in mail view.

Allow users to only sync selectively from an account (ie, ONLY Mail, Only Calendar, ONLY Contacts, ONLY Google Drive and not email...) as opposed to having to sync mail, calendar, contacts as a whole.

Allow users to only sync some folders.

To move messages to different folders or to peek a message.

It would be nice to be able to control what types of items create notification banners/alerts. For example I only want to see calendar reminders but not an alert for new emails.

Ability to sync my settings across devices.

It would be extremely helpful to be able to attach files from other applications (at least other Microsoft apps) to an email. It is very inconvenient to have to transfer a spreadsheet or word document to Dropbox and then attach it to an email thread in order to save the integrity of the thread.