You may have already seen some new options when sharing links to files in SharePoint (and OneDrive). Here’s what’s available in my tenant today:
If you use the “Anyone with the link” option (for anonymous access) you can choose a date on which the link will expire and access will no longer be granted via that link.
You can block people from downloading only if you uncheck “Allow editing” for the link types that support it.
Your basic options are to allow anonymous users (with or without an expiration date) to:
- Edit & Download
- View & Download
- View Only
You can also easily share with people only in your tenant, even if they don’t have prior access, and choose whether they can edit, view and download, or just view.
People with existing access is useful just to Skype/Teams someone a quick link to get to the file. Their pre-existing permissions apply.
Finally, “Specific People” can allow you to share with external users but they must use the address you share with, as they’ll be sent a verification code to validate their identity. This adds a layer of security to otherwise anonymous share links.
Enter addresses you’re sharing the file with and click send or copy the URL to share through another avenue. 
The user receives an email with a link that takes them to a page to validate the email address. 
Then they’re emailed a unique security code to validate their identity/ownership of the email address.
Note: You may not be prompted to enter your email address if opened directly. But if the email is forwarded, user will be asked to verify email before they’re able to send a code.