Modular pet structure assemblies and related methods are disclosed. The modular pet structures have a base module with a plurality of connection joints for receiving other modules. The base can receive one or more than one vertical modules. The vertical module can attach to the base and includes at least one bi-directional movement mechanism having two spaced apart ends. The at least one bi-directional movement mechanism is configured to move when one of the ends is moved. For example, when a toy attached to one end is moved, a second toy attached to the other end moves in response thereto.
