Wireless information networks have become a necessity of our day-today life. Over a billion Wi-Fi access points, hundreds of thousands of cell towers, and billions of IoT devices, using a variety of wireless technologies, create the infrastructure that enables this technology to access everyone, everywhere. The radio signal carrying the wireless information, propagates from antennas through the air and creates a radio frequency (RF) cloud carrying a huge amount of data that is commonly accessible by anyone. The big data of the RF cloud includes information about the transmitter type and addresses, embedded in the information packets; as well as features of the RF signal carrying the message, such as received signal strength (RSS), time of arrival (TOA), direction of arrival (DOA), channel impulse response (CIR), and channel state information (CSI). We can benefit from the big data contents of the messages as well as the temporal and spatial variations of their RF propagation characteristics to engineer intelligent cyberspace applications. This paper provides a holistic vision of emerging cyberspace applications and explains how they benefit from the RF cloud to operate. We begin by introducing the big data contents of the RF cloud. Then, we explain how innovative cyberspace applications are emerging that benefit from this big data. We classify these applications into three categories: wireless positioning systems, gesture and motion detection technologies, and authentication and security techniques. We explain how Wi-Fi, cell-tower, and IoT wireless positioning systems benefit from big data of the RF cloud. We discuss how researchers are studying applications of RF cloud features for motion, activity and gesture detection for human-computer interaction, and we show how authentication and security applications benefit from RF cloud characteristics.