Novel solutions are required to connect billions of devices to the network as envisioned by the IoT. In this article we propose to use LiFi, which is based on off-the-shelf LEDs, as an enabler for the IoT in indoor environments. We present LiFi4IoT, a system which, in addition to communication, provides three main services that the radio frequency (RF) IoT networks struggle to offer: precise device positioning; the possibility of delivering power, since energy can be harvested from light; and inherent security due to the propagation properties of visible light. We analyze the application space of IoT in indoor scenarios, and propose a LiFi4IoT access point (AP) that communicates simultaneously with IoT devices featuring different types of detectors, such as CMOS camera sensors, PDs, and solar cells. Based on the capabilities of these technologies, we define three types of energy self-sufficient IoT "motes" and analyze their feasibility. Finally, we identify the main research directions to enable the LiFi4IoT vision and provide preliminary results for several of these.