Sparse representation can efficiently model signals in different applications to facilitate processing. In this article, we will discuss various applications of sparse representation in wireless communications, with focus on the most recent compressive sensing (CS) enabled approaches. With the help of the sparsity property, CS is able to enhance the spectrum efficiency and energy efficiency for the fifth generation (5G) networks and Internet of Things (IoT) networks. This article starts from a comprehensive overview of CS principles and different sparse domains potentially used in 5G and IoT networks. Then recent research progress on applying CS to address the major opportunities and challenges in 5G and IoT networks is introduced, including wideband spectrum sensing in cognitive radio networks, data collection in IoT networks, and channel estimation and feedback in massive MIMO systems. Moreover, other potential applications and research challenges on sparse representation for 5G and IoT networks are identified. This article will provide readers a clear picture of how to exploit the sparsity properties to process wireless signals in different applications.