Efforts in performance analysis of Code Division Multiple Access (CDMA) systems have concentrated on obtaining asymptotic approximations and bounds for system error probabilities. As such, these cannot capture the sensitivities of the system performance to any class of parameters, and the optimization of such systems (with respect to any class of parameters) presents itself to no analytical solutions. A discrete event dynamic systems (DEDS) formulation is developed for CDMA systems whereby the sensitivity of the average probability of error can be evaluated with respect to a wide class of system parameters via sample path based gradient estimation techniques like infinitesimal perturbation analysis (IPA) and the likelihood ratio (LR) method. Appropriate choice of the sample path and the corresponding sample performance function leads to analyzing the sensitivity of the average probability of error to near-far effects, power control, and code parameters. Further, these sensitivity analysis methods are incorporated in gradient algorithms for optimizing system performance in terms of the minimum probability of detection error. Specifically, for direct-sequence CDMA systems, IPA based stochastic gradient algorithms are used to develop a class of adaptive linear detectors that are optimum in that they minimize the average probability of bit-error. These detectors outperform both the matched filter and MMSE detectors, and also alleviate the disadvantage of multiuser detection schemes that require implicit information on the multiple access interference. For CDMA systems in the optical domain, IPA based stochastic algorithms are used to develop a class of adaptive threshold detectors that minimize the average probability of bit-error. These detectors outperform the correlation detector and also preclude the need for assumptions on the interference statistics required by existing optimum one-shot detectors. All adaptive detection schemes developed here are easily implementable owing to the simple recursive structures that arise out of our sample realization based approach. The sequential versions of the adaptive detectors developed in here require no preamble, which makes them a viable choice for CDMA channels subject to temporal variations due to dispersion effects and variable number of users in the channel.