I need to have a team reviewing documents but don't want them to save it on their PC's. I know you can open it up and work it then when it saves it will save back on SharePoint. Is there a way to allow them to do so but restrict it for saving on to the PC?
First, to prevent users from downloading the content to local PC, you could set "Offline Client Availability" to "No" at site settings.
Second, you could enable Office Web Apps / Office Online Server to provide co-authoring over the browser.
You didn't clarify whether you are using SharePoint Online or SharePoint On-premise. With SharePoint Online, documents with common Office file types can be opened on the browser when it's just set as the default opening behavior. With SharePoint On-premise, you need to have Office Web Apps installed and configured besides setting the default opening behavior.
For the review-requirement: It depends whether the download should be disabled for all, or only for the reviewers. Also if by reviewing you only mean that users can open the document (in their browser), read it through, and leave it as it is, the following is what you should do. If reviewing means something else for you, then you need to clarify your question.
If you want to have the Download-feature completely disabled in your document library, go to the library's Settings > Advanced Settings and on Allow items from this document library to be downloaded to offline clients? select No. This will prevent the downloading of the document for all users.
If the download-option should still be available for e.g. Full Control users, then you need to assign the built-in permission level View Only to your users doing the review in your document library. With View Only, users do not have a permission to download the documents to their computers.
If you have enabled 'Publishing' on a SharePoint 2013 site collection you could use the Restricted Read permission level; this is an OOTB SharePoint group on Publishing sites. This Microsoft page has info about SP groups, including Restricted Read.
Warning - activating Publishing on your SharePoint site might have some unintended consequences, so please fully inform yourself before activating Publishing. Here is a blog post on Publishing should you need some background info.