In this thesis, we first present a variance estimation technique based on the standardized time series methodology for steady-state simulations. The proposed variance estimator has competitive bias and variance compared to the existing estimators in the literature. We also present the technique of rebatching to further reduce the bias and variance of our variance estimator. Second, we present two fully sequential indifference-zone procedures to select the best system from a number of competing simulated systems when best is defined by the maximum or minimum expected performance. These two procedures have parabola shaped continuation regions rather than the triangular continuation regions employed in several papers. The rocedures we present accommodate unequal and unknown ariances across systems and the use of common random numbers. However, we assume that basic observations are independent and identically normally distributed. Finally, we present procedures for finding a set of feasible or near-feasible systems among a finite number of simulated systems in the presence of multiple stochastic constraints, especially when the number of systems or constraints is large.