Graphene is a promising candidate for optoelectronic and fast electronics research. In THz and sub-THz frequency regime, sensitive detectors are very difficult to make. This dissertation presents my Ph.D study of THz sources and THz/Microwave (MW) detectors made with graphene. My work demonstrates the emission and detection of 1.9 THz radiation from graphene coupled to a double-patch antenna and a silicon lens. More than 3 orders of magnitude performance improvements are achieved in a half-edge-contacted graphene thermoelectric (TE) detector operating at 1.9 THz by antenna coupling and Si lens coupling. The thermoelectric mechanism is also employed in MW detection. A heterodyne TE microwave mixer at room temperature with 50 GHz (minimum) IF bandwidth is demonstrated. Currently Golay cells and pyroelectric detectors are commonly used as room temperature detectors for THz, my experimental results represent a significant advance toward practically useful graphene THz detectors. By optimizing the device structure, graphene detectors will have similar responsivity, lower NEP and are much faster, thus having a potential to revolutionize THz detection technology and industry. The demonstrated wide band Graphene MW mixer will pave the way for commercializing graphene-based high-speed electronic devices.