This thesis presents innovative approaches for controlling the False Discovery Rate (FDR) in both high-dimensional statistical inference and finite-sample cases, addressing challenges arising from various dependency structures in the data. The first project introduces novel multiple testing methods for matrix-valued data, motivated by an electroencephalography (EEG) experiment, where we model the inherent complex row-column cross-dependency using a matrix normal distribution. We proposed two methods designed for structured matrix-valued data, to approximate the true FDP that captures the underlying cross-dependency with statistical accuracy. In the second project, we focus on simultaneous testing of multivariate normal means under diverse covariance matrix structures. By adjusting p-values using a BH-type step-up procedure tailored to the known correlation matrix, we achieve robust finite-sample FDR control. Both projects demonstrate superior performance through extensive numerical studies and real-data applications, significantly advancing the field of multiple testing under dependency. The third project presented exploratory simulation results to demonstrate the methods constructed based on the paired-p-values framework that controls the FDR within the multivariate normal means testing framework. / Statistics