In this article we first summarize some of the most recent HetNet mobility studies for LTEAdvanced, and use these to highlight the challenges that should be further addressed in the research community. A state-of-the-art HetNet scenario with macros and small cells deployed on different carriers, while using inter-site carrier aggregation, is hereafter studied. Hybrid Het- Net mobility solutions for such cases are derived, where macrocell mobility is network controlled, while small-cell mobility is made UE-autonomous. The proposed scheme is characterized by having the UE devices autonomously decide small cell addition, removal, and change without any explicit signaling of measurement events to the network or any signaling of hand - over commands from the network. Hence, the proposed solution effectively offloads the network from having to perform frequent small cell handoff decisions, and reduces the signaling overhead compared to known network controlled mobility solutions. Results from extensive dynamic system-level simulations are presented to demonstrate the advantages of the proposed technique, showing significant savings in signaling overhead.