Numerical simulations for solving fermionic quantum many-body systems are notoriously challenging, especially in the presence of significant correlations. Many approaches start from mean-field approximations and are therefore limited in their applicability, particularly when studying quantum dynamics. In this talk, I will introduce novel numerical techniques based on neural quantum states and variational Monte Carlo to capture eigenstates and quantum dynamics of fermionic systems. I will present new variational approaches for fermionic time-dependent wave functions, surpassing mean-field approximations to capture many-body correlations effectively. Specifically, I will focus on quantum many-electron systems, crucial for applications such as predicting electronic structures in quantum chemistry, properties of crystalline solids, and behaviors of complex materials.