sentences: The exponential growth and availability of data in all forms is the main booster to the continuing evolution in the communications industry. The popularization of traffic-intensive applications including high definition video, 3-D visualization, augmented reality, wearable devices, and cloud computing defines a new era of mobile communications. The immense amount of traffic generated by today's customers requires a paradigm shift in all aspects of mobile networks. Ultradense network (UDN) is one of the leading ideas in this racetrack. In UDNs, the access nodes and/or the number of communication links per unit area are densified. In this paper, we provide a survey-style introduction to dense small cell networks. Moreover, we summarize and compare some of the recent achievements and research findings. We discuss the modeling techniques and the performance metrics widely used to model problems in UDN. Also, we present the enabling technologies for network densification in order to understand the state-of-the-art. We consider many research directions in this survey, namely, user association, interference management, energy efficiency, spectrum sharing, resource management, scheduling, backhauling, propagation modeling, and the economics of UDN deployment.