This paper introduces new single-loop algorithms developed for component and system reliability-based design and topology optimization. A single-loop reliability-based design/topology optimization (RBDO/RBTO) algorithm replaces the inner-loop iterations that evaluate probabilistic constraints by a non-iterative approximation. The proposed single-loop algorithms account for statistical dependence between the limit-states by using a matrix-based system reliability (MSR) method to compute the system failure probability and its parameter sensitivities. The SRBTO/MSR approach is applicable to general system events including series, parallel, cut-set and link-set systems and provides the gradients of the system failure probability to facilitate gradient-based optimization. In most RBTO applications, probabilistic constraints are evaluated by use of the first-order reliability method (FORM) for efficiency. In order to improve the accuracy of the reliability calculations for RBDO or RBTO problems with high nonlinearity, we introduce a new single-loop RBDO scheme utilizing the second-order reliability method (SORM). Moreover, in order to overcome challenges in applying the proposed algorithm to computationally demanding topology optimization problems, we utilize the multiresolution topology optimization (MTOP) method, which achieves computational efficiency in topology optimization by assigning different levels of resolutions to three meshes representing finite elements, design variables, and material density distribution, respectively. The paper provides a numerical example of three-dimensional topology optimization to demonstrate the proposed CRBTO and SRBTO algorithms and applications. Monte Carlo simulations are also performed to verify the accuracy of the failure probabilities computed by the proposed approach.