Light-matter interaction is always one of the themes of science. With the rapid development of ultra-short and ultra-strong laser techniques, nowadays we can research the internal world in a single atom and control the light-electron interactions to explore the ultrafast dynamics of intra-atomic electrons. Laser-induced tunneling ionization of atoms, as the footstone of many strong-field physical phenomena, has important research significance and is also one of the hot frontier topics. In this paper, we review the recent research advances in strong-field atomic tunneling ionization. The coordinate and momentum distributions of electrons after tunneling process are obtained based on the non-adiabatic tunneling ionization in the natural coordinates (i.e., the parabolic coordinates). We introduce the theoretical description and experimental measurement methods for the initial phase (i.e., the sub-barrier phase) of electrons obtained in the tunneling process. Based on the sub-barrier phase, we can reveal the quantum dynamical information of the tunneling process. We introduce the recent advances in photoelectron spin polarization during the strong-field tunneling ionization. On the basis of the orthogonal two-color fields, the degrees of freedom of photoelectrons in the time and space dimensions can be accurately controlled. Finally, we summarize this paper and predict future research advances.