Energy efficiency is a growing concern in every aspect of the technology. Apart from maintaining profitability, energy efficiency means a decrease in the overall environmental effects, which is a serious concern in today's world. Using a femtocell in Internet of Things (IoT) can boost energy efficiency. To illustrate, femtocells can be used in smart homes, which is a subpart of the smart grid, as a communication mechanism in order to manage energy efficiency. Moreover, femtocells can be used in many IoT applications in order to provide communication. However, it is important to evaluate the energy efficiency of femtocells. This paper investigates recent advances and challenges in the energy efficiency of the femtocell in IoT. First, we introduce the idea of femtocells in the context of IoT and their role in IoT applications. Next, we describe prominent performance metrics in order to understand how the energy efficiency is evaluated. Then, we elucidate how energy can be modeled in terms of femtocell and provide some models from the literature. Since femtocells are used in heterogeneous networks to manage energy efficiency, we also express some energy efficiency schemes for deployment. The factors that affect the energy usage of a femtocell base station are discussed and then the power consumption of user equipment under femtocell coverage is mentioned. Finally, we highlight prominent open research issues and challenges.