The last few decades have witnessed the extraordinary advances in theoretical and experimental tools, which have enabled the manipulation and monitoring of ultrafast dynamics with high precisions. For modeling dynamical responses beyond the perturbative regime, computational methods based on time-dependent density functional theory (TDDFT) are the optimal choices. Here, we introduce TDAP (time-dependent ab initio propagation), a first-principle approach that is aimed at providing robust dynamic simulations of light-induced, highly nonlinear phenomena by real-time calculation of combined photonic, electronic, and ionic quantum mechanical effects within a TDDFT framework. We review the implementation of real-time TDDFT with numerical atomic orbital formalisms, which has enabled high-accuracy, large-scale simulations with moderate computational cost. The newly added features, i.e., the time-dependent electric field gauges and controllable ionic motion make the method especially suitable for investigating ultrafast electron-nuclear dynamics in complex periodic and semiperiodic systems. An overview of the capabilities of this first-principle method is provided by showcasing several representative applications including high-harmonic generation, tunable phase transitions, and new emergent states of matter. The method demonstrates a great potential in obtaining a predictive and comprehensive understanding of quantum dynamics and interactions in a wide range of materials at the atomic and attosecond space-time scale.