In Office365 there are several admin roles. This article gives an overview and a comparison among different roles. However up to now one major problem we had was that there was no application / workload specific admin role. So it was not possible to assign an Exchange Admin or a SharePoint Admin.
Finally Microsoft is releasing this much awaited Workload –specific admin roles in to Office365. Here is the introduction from MS;
“Workload-specific admin roles will provide more flexibility to organizations that want to structure admin access to Exchange Admin Center, SharePoint Admin Center, and Lync Admin Center. For example, an Exchange admin will no longer require Office 365 global admin rights to manage Exchange Online.”
This is still rolling out so may take sometime to appear in your tenant.