Balmer-dominated shocks in supernova remnants (SNRs) produce strong hydrogen lines with a two-component profile composed of a narrow contribution from cold upstream hydrogen atoms, and a broad contribution from hydrogen atoms that have undergone charge transfer reactions with hot protons. Observations of emission lines from edge-wise shocks in SNRs can constrain the gas velocity and collisionless electron heating at the shock front. Downstream hydrogen atoms engage in charge transfer, excitation and ionization reactions, defining an interaction region called the shock transition zone, with characteristic width l_zone ∼ 10^{15} cm, for shock velocity v_s ∼ 1000 km s^{−1} and upstream density n_0 ∼ 1 cm^{−3}. The properties of hot hydrogen atoms undergoing charge transfer (called broad neutrals) are critical for accurately calculating the structure and radiation from the shock transition zone. I discuss recent work describing the kinetic, fluid and emission properties of Balmer-dominated shocks, and our method to properly treat the effect of broad neutral kinetics on shock transition zone structure. We use our models to extract shock parameters from observations of Balmer-dominated SNRs. We find that inferred shock velocities and electron temperatures are systematically lower (by ∼ 30−50%) than those of previous calculations. Our results have a strong dependence on the ratio of electron to proton temperatures, \beta = T_e/T_p. We construct a relation \beta(v_s) between the temperature ratio and shock velocity and show that post-shock electrons are heated to higher temperatures at larger shock velocities, contrary to the velocity independent heating mechanism proposed by Ghavamian et al. (2007b).