In this work, capturing Near-Earth Asteroids (NEAs) into Near-Earth orbits is investigated. A general optimization strategy is employed whereby a genetic algorithm is used to seed a sequential quadratic programming (SQP) method for the first step, and then nearby solutions seed further SQP runs. A large number of solutions are produced for several asteroids with varying levels of thrust, and under the effects of various perturbations. Solutions are found over a range of epochs and times of flight as opposed to many traditional methods of optimizing point solutions. This methodology proved effective, finding low-thrust capture solutions within 10% of the required Delta V for analytically estimated transfers, and matching results from other optimization programs such as MALTO. It is found that the effects of solar radiation pressure (SRP) and n-body effects do not have a significant impact on the optimized transfer costs, nor do the perturbations significantly affect the shapes and trends of the optimized solution space. <p><br></p> <p>These optimized results are then used to develop analytic models for both optimized transfer costs and flight times. These models are then used to estimate the transfer costs and flight times for all listed Near Earth Asteroids from the JPL Small Body Database. This analysis is then used to determine the nominal properties of potentially capturable asteroids. The characteristics are then related to a series of different asteroid transfer technologies, elucidating each technology's capabilities and potential capture targets. Finally, this analysis concludes with a brief roadmap of the major decisions mission designers should consider for future asteroid capture missions.</p>