Screenshot: Tumblr
Tumblr is tweaking the way reblogs work on its platform. The company has started to roll out reblog controls on the web and iOS, with Android to follow. This will allow users to prevent other Tumblr users from reblogging a post they made. According to Tumblr, it made this feature available at the request of users. It's meant to give them a sense of safety and an improved posting experience on the platform.
So, if you block someone on Tumblr, they will not be able to reblog a post. As The Verge pointed out, there will be ways to work around this (like screenshots). But it does give you some control over how your content spreads and who engages with it on the website.