The spatial structure of base stations (BSs) in cellular networks plays a key role in evaluating the downlink performance. The BSs are usually assumed to form a lattice or a Poisson point process (PPP). In reality, however, they are deployed neither fully regularly nor completely randomly. Accordingly, in this thesis, we first use different spatial stochastic models, including the PPP, the Poisson hard-core process (PHCP), the Strauss process (SP), and the perturbed triangular lattice, to model the spatial structure by fitting them to the locations of BSs in real cellular networks obtained from a public database. We propose the coverage probability (the probability that the signal-to-interference-plus-noise-ratio (SINR) exceeds a threshold) as the criterion for the goodness-of-fit, and provide two general approaches for fitting. One approach is fitting by the method of maximum pseudolikelihood. As for the fitted models, the SP provides a better fit than the PPP and the PHCP. The other approach is fitting by the method of minimum contrast that minimizes the average squared error of the coverage probability. This way, fitted models are obtained whose coverage performance matches that of the given data set very accurately.  Second, we consider the very general class of motion-invariant point processes as models for the BSs and theoretically analyze the behavior of the outage probability. (complement of the coverage probability). We show that, remarkably, the slope of the outage probability (in dB) as a function of the threshold (also in dB) is the same for essentially all motion-invariant point processes, as the threshold goes to zero. The slope merely depends on the fading statistics. Using this result, we introduce the notion of the asymptotic deployment gain (ADG), which characterizes the horizontal gap between the coverage probability of the PPP and another point process in the high-reliability regime (where the coverage probability is near 1). To demonstrate the usefulness of the ADG for the characterization of the coverage, we investigate the coverage probabilities and the ADGs for different point processes and fading statistics by simulations.