Terms of use may change, so you should always check the most up-to-date terms of service. Tumblr was acquired by Yahoo in 2013. While Flickr, which is also owned by Yahoo, uses Yahoo’s Terms of Service, Tumblr has its own Terms of Service, which as of December 2016 state that users retain ownership in any intellectual property rights to content they post to Tumblr, and grant Tumblr a “non-exclusive, worldwide, royalty-free, sublicensable, transferable right and license to use, host, store, cache, reproduce, publish, display (publicly or otherwise), perform (publicly or otherwise), distribute, transmit, modify, adapt (including, without limitation, in order to conform it to the requirements of any networks, devices, services, or media through which the Services are available), and create derivative works of” the content.
This seemingly very broad license is further clarified by stating that these rights are granted “for the limited purposes of allowing Tumblr to operate the Services in accordance with their functionality, improve the Services, and develop new Services.” In particular, the right to create derivative works “is not intended to give Tumblr a right to make substantive editorial changes or derivations, but does, for example, enable reblogging.”
In addition, the license “includes the right for Tumblr to make all publicly-posted Content available to third parties selected by Tumblr, so that those third parties can syndicate and/or analyze such Content on other media and services.” Tumblr gives the example of licensing a live feed of all public Tumblr activity to search engines.