The gravitational interactions of planets in multiplanetary systems can have effects ranging from tiny orbital alterations to severe instability and everything in between. In this thesis, I discuss three applications of planet-planet interactions. First, I demonstrate using N-body simulations that a commonly-used analytical approximation can have large inaccuracies for planetary systems like those observed by the Kepler mission when used to calculate the rate at which the longitude of the ascending node changes. The dependency between the eccentricity, inclination, and semi-major axis ratio (α) of a pair of planets requires a higher-order expansion of the disturbing function, particularly in α to recreate the simulated behavior to a specified accuracy. Not accounting for these effects could lead to significant errors when calculating the locations of secular resonances, as I demonstrate with the Kepler-117 system. Secondly, I use N-body simulations and analytics to illustrate how the slight change in period ratio over time for planet pairs both in and out of mean-motion resonance can lead to observable sculpting of the time-averaged period ratio for a population of planets. The strength of this sculpting depends on the eccentricity of the planets involved, and we can use the observed period ratio distribution from the Kepler mission to infer the distribution of eccentricity for those planets. When modeled as an independent Rayleigh distribution for each planet, I find the Rayleigh scale parameter is σe < 0.245 (near the 3:1 resonance) and σe < 0.095 (5:3) with 95% confidence. Lastly, I endeavor to quantify how the presence of two giant planets affects the potential habitability of an Earth-like planet. Stability predictions, on both long and short timescales, are combined with the maximum eccentricity for Earth-like planets located near the expected habitable zone and a probabilistic habitability model to assess the relative habitability for each giant planet configuration—that is, the integrated habitability probability compared to a system with only an Earth-like planet. By varying the properties of the two giant planets (mass, semi-major axis, eccentricity, and inclination), I identify correlations between various parameters, identify particularly habitable and uninhabitable configurations, and demonstrate how the interplay of mean-motion resonance, secular resonances, and other dynamical effects must be taken into account when considering habitability.