It has been reported that some specially designed recurrent neural networks and their related neural dynamics are efficient to solve quadratic programming (QP) problems in the real domain. A complex-valued QP problem is generated if its variable vector is composed of the magnitude and phase information, which is often depicted in time-dependent form. Given the important role that complex-valued problems play in cybernetics and engineering, computational models with high accuracy and strong robustness are urgently needed, especially for time-dependent ones. However, the research on online solution of time-dependent complex-valued problems has been much less investigated than that of time-dependent real-valued problems. In this chapter, to solve online time-dependent complex-valued quadratic programming problems subject to linear constraints, two new discrete-time neural dynamics models are given and investigated, which can achieve global convergence performance in the presence of perturbations with theoretical analyses provided. In addition, the secondly designed model is developed to eliminate the operation of explicit matrix inversion by introducing the quasi-Newton Broyden-Fletcher-Goldfarb-Shanno method (BFGS) to approximate its inverse matrix. Moreover, computer simulation results and applications to robotics and filters are provided to illustrate the feasibility and superiority of the constructed models, with comparisons to the existing solutions.