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Intense laser-plasma interaction, generally characterized by focused laser intensities exceeding ~1 TW/cm2, is a major pillar of plasma physics and nonlinear optics with broad applications, including high energy charged particle and photon sources, the generation and study of high energy density physics conditions, fusion energy sources, remote detection techniques, and self-guided nonlinear propagation. For many important applications, longer wavelength lasers provide favorable scaling for laser-plasma interactions, and in several cases enable entirely new phenomena. In this dissertation we present experimental and computational results for three laser-plasma-based applications using ultrashort mid-infrared (mid-IR or MIR) and long-wave-infrared (LWIR) laser pulses. In the first laser wakefield acceleration (LWFA) experiment at mid-IR wavelengths, we demonstrate acceleration of electron bunches driven by relativistic self-focusing collapse of mid-IR laser pulses in near-critical density gas jet targets, and compare scaling of bunch charge and energy to those from common near-infrared systems. Second, we demonstrate that single-electron-seeded avalanche breakdown driven by picosecond mid-IR lasers is an ultrasensitive technique for measuring extremely low plasma densities in gases. We use this technique in two applications. First, we first demonstrate standoff detection of radioactive materials, with avalanche measurements enabling determination of source location and estimates of the radioactivity level. We then use the technique to measure ionization yield induced by an auxiliary laser in atmospheric pressure range gases over 14 orders of magnitude, a record range achievable with no other technique we are aware of. Finally, we present theory and simulations of nonlinear propagation of high power MIR and LWIR multi-picosecond pulses in air, demonstrating that self-guided propagation at moderate intensity is mediated by an ensemble of discrete avalanche plasmas seeded by aerosols.