Cellular mobile networks are used by more than 4 billion users worldwide. One effective way to meet the increasing demand for data rates is to deploy femtocells, which are low-power base stations that connect to the mobile operator through the subscriber's residential Internet access. Yet, security and privacy issues in femtocell-enabled cellular networks, such as UMTS and LTE, still need to be fully addressed by the standardization bodies. In this paper, we review significant threats to the security and privacy of femtocell-enabled cellular networks. We also propose novel solution directions in order to tackle some of these threats by drawing inspiration from solutions to similar challenges in wireless data networks such as WLANs and mobile ad hoc networks (MANETs).