Communication links operating at terahertz frequencies are envisioned to provide a revolutionary enhancement of data transmission. As fundamental building blocks, waveguides play an indispensable role in future terahertz networks, not only transporting data streams with unprecedented data rates, but also serving as a versatile platform for signal processing. Among various terahertz waveguides, metal-wire waveguides have attracted particular attention due to their distinct characteristics, such as structural simplicity, broad operating bandwidths, low transmission losses, and low dispersion, in turn making them promising candidates for signal processing. However, because of the tight confinement of modal energy within the wavelength-scale space, manipulating the propagating terahertz signals in-between the metal-wires is challenging. Here, we report the most recent advances in the realization of signal-processing functionalities within metal-wire waveguides. Based on these state-of-the-art methodologies, broadband signal processors that can function as filters, couplers, temporal integrators, as well as multiplexers, have been obtained. We expect this review to inspire new terahertz metal-wire signal processors with high potential for real-time tunability and reconfigurability.