Conventionally, the performances of Analog and Mixed-Signal (AMS) circuits have been characterized using specification-based functional tests. In these test methods, the correct functionalities of AMS circuits are verified by measuring pre-determined specification parameters of AMS circuits. The conventional test methods provide accurate test results by using various test equipments which generate functional test signals and capture the test responses externally. However, due to rapid increase in the performance of AMS circuits in recent years, the conventional test methods face various challenges in the aspects of test cost, test time and testability. The goal of this dissertation is to develop innovative functional test methods for AMS circuits which are aimed at reducing the test cost and test time while providing comparable test accuracy to the conventional test methods. To achieve this goal, efforts have been made to explore the characteristics of AMS circuits in a system level and to research efficient performance characterization methods based on the system level modeling of Devices Under Test (DUTs). As a part of these efforts, the pseudorandom test methods for nonlinear AMS circuits have been developed. In these methods, the pseudorandom signal is used to excite the DUT and to generate the test response which has sufficient information to characterize DUT performances. The pseudorandom test methods use the Volterra series model to capture the nonlinear behaviors of AMS circuits and to calculate various specification parameters of the DUT using the pseudorandom test response. In doing so, the performances of nonlinear AMS circuits can be characterized straightforwardly and accurately using a low-cost test setup. Also, in an effort to reduce the test time, parallel test methods of AMS circuits have been developed in which multiple DUTs are tested simultaneously by sharing a common test setup. In these methods, the test responses generated from different DUTs are combined together and the resulting composite test response is used to characterize the performance of each DUT individually. This will reduce the use of tester resources and will increase the test throughput beyond the level limited by the test equipments. The spectral characteristics of test stimulus are studied along with the system level behavior of AMS circuits to develop the efficient parallel test methods. Finally, in order to consider the practical issue of generating at-speed test stimuli for high-speed DUTs using a low-cost test setup, a reconfigurable built-off test interface is developed which can be used to generate various test patterns, including high-speed pseudorandom signal, using a low-speed tester. / text