  The macroscopic electromagnetic properties of type II superconductors are
primarily influenced by the behavior of microscopic superconducting flux
quantum units. Time-dependent Ginzburg-Landau (TDGL) equations provide an
elegant and powerful tool for describing and examining both the statics and
dynamics of these superconducting entities. They have been instrumental in
replicating and elucidating numerous experimental results over the past
decades.This paper provides a comprehensive overview of the progress in TDGL
simulations, focusing on three key aspects of superconductor applications. The
initial section delves into vortex rectification in superconductors described
within the TDGL framework. We specifically highlight the superconducting diode
effect achieved through asymmetric pinning landscapes and the reversible
manipulation of vortex ratchets with dynamic pinning landscapes. The subsequent
section reviews the achievements of TDGL simulations concerning the critical
current density of superconductors, emphasizing the optimization of pinning
sites, particularly vortex pinning and dynamics in polycrystalline Nb$_3$Sn
with grain boundaries. The third part concentrates on numerical modeling of
vortex penetration and dynamics in superconducting radio frequency (SRF)
cavities, including a discussion of superconductor insulator superconductor
multilayer structures. In the last section, we present key findings, insights,
and perspectives derived from the discussed simulations.
