Intense laser-plasma interactions, generally characterized by focused laser intensities exceeding several TW per cm2, are of basic and applied interest in a number of areas, including the generation of relativistic charged-particle beams, high-energy photon generation, and nonlinear optics extending to the relativistic regime. Mid-infrared (mid-IR) lasers provide favorable wavelength scaling of various laser-plasma interaction parameters compared to commonly used near-infrared systems, and in several cases enable entirely new phenomena. In this talk I will present our experimental and computational results relating to three laser-plasma-based applications using ultrashort mid-IR and long-wave-IR laser pulses. First, we demonstrate self-modulated laser wakefield acceleration driven by mid-IR laser pulses collapsing in near-critical-density targets and discuss scaling from common near-infrared systems. Second, we demonstrate that electron avalanche breakdown driven by picosecond, mid-IR lasers create discrete breakdowns from individual seed electrons, providing a unique and extremely sensitive method of detecting ultralow plasma densities in gases. We apply this technique to demonstrate standoff detection of radioactive materials and to measure laser ionization yield in atmospheric pressure-range gases over an unprecedented 14 orders of magnitude. Finally, we present a theory of self-guiding for high-power mid-infrared and long-wave-infrared multi-picosecond pulses interacting with discrete avalanche breakdown sites and show through propagation simulations that aerosol-initiated avalanches support laser self-guiding at moderate intensities.