Apparatuses and methods associated with block structure and robot cooperation are disclosed herein. In embodiments, a block apparatus may include a block structure-robot coordination module to cooperate with one or more robots to affect operations of the one or more robots relative to at least a block structure which the block apparatus is a member. The block apparatus may further include a housing that houses the block structure-robot coordination module, with features to mate the block apparatus with one or more other blocks to cause the block apparatus to become a member of the block structure. In embodiments, a robot may include control module to control a number of actuators to operate one or more features to perform one or more operations relative to the block structure. Other embodiments may be described and/or claimed.