Laser spectroscopy in the mid-infrared (IR) and terahertz (THz) spectral regions is of particular interest since it gives access to the fundamental rovibrational bands of many molecules as well as to molecular rotational bands and lattice vibrations in solid-state samples. Among all modern laser technologies, optical frequency combs have emerged as the most promising sources for high-resolution spectrometers with broadband spectral coverage. We provide an overview of recent advancements in electrically pumped quantum- and interband-cascade-laser (QCL and ICL) frequency combs operating in the mid-IR and THz regions as an important step towards field applications with truly integrated and scalable frequency-comb technology. We also discuss dual-comb spectroscopy techniques that offers fast chemical sensing without the need for optomechanical tuning or dispersive spectrometers, and provide an overview of the spectroscopic capabilities provided by QCL and ICL dual-comb spectrometers. Measurement approaches and recent experimental implementations of mid-IR and THz dual-comb spectroscopy of chemicals by various research groups using QCL and ICL frequency-comb technology are discussed