Next generation wireless systems are expected to intelligently connect everything around us allowing us to sense, interface and control the digital world we live in and forming the "Internet of Things" (IoT). Low-energy, maintenance-free wireless transmitters that can sporadically access the spectrum are key enablers for this vision. In this talk, we will investigate two novel communication problems introduced by this paradigm. We will first focus on communication with wireless transmitters that do not have traditional batteries but can harvest their energy from the natural resources in their environment. Building such transmitters has been of significant recent interest, motivated by their promise to sustain energy self-sufficient and maintenance-free operation. We will then discuss sporadic low-energy massive random access for IoT networks and design new random access codes by connecting this problem to the so called group testing problem.