Mid-Infrared (Mid-IR) and Terahertz(THz) spectrum, ranging from 10 um to 6 mm in wavelength, is the focus of basic research in solid-state physics, chemistry, materials science, as well as applications in next-generation communications, far-infrared bolometer, bio-/chemical sensing, and medical imaging. This wavelength range is at the intersection between photonics and electronics, presenting tremendous opportunities to boost fundamental light-matter interactions enabled by plasmonic nanostructures, metamaterials, and inherent molecular vibrational modes, which occur on time scales of tens of femtoseconds to picoseconds. Here, I will introduce Mid-IR and THz time-domain spectroscopy based on an ultrafast femtosecond pulse laser to enable highly sensitive and selective Mid-IR and THz spectroscopic applications with plasmonic nanogaps. These next generation spectroscopic applications will bring a great impact in the advancement of ultra-small quantity detection of explosives, ultrafast transport for superconducting thin films, and conformational dynamics of biomolecules in their aqueous environment.