One of the aspects of going to "the cloud" with my corporate account that I had to adjust to was the 64k rule limit for Outlook/OWA.
It limited the amount of rules I could create and process, and I had quite a few due to being a "filer" more than a "piler" for e-mail.
On a good note, you can now increase your rule limit to 256k for your Office 365 tenants.
On my friends and family tenant, I just had to execute "set-mailbox -identity firstname.lastname@example.org -RulesQuota 256kb".
The "living document" related to this feature can be access here.