In this dissertation, we theorize the fundamentals of an ultrafast and ultrastrong optical field interacting with graphene and graphene-like nanocrystals as a prototype of two-dimensional class of materials. Graphene exhibits dramatically different characteristics from both insulators and metals. Field- induced, Zener-type electron transfer from the valence band to the conduction band is deeply irreversible (nonadiabatic) in graphene. Correspondingly, an ultrashort electronic current can be induced on a femtosecond timescale. The ultrafast optically-induced current and charge transfer in graphene may provide a fundamental basis for detection and calibration of ultrashort intense laser pulses and are promising for petahertz information processing. We further studied and proposed techniques to manifest the topological properties of graphene using the few-cycle circularly polarized pulse. Our findings hold application in spectroscopy, imaging, laser technology, transmitting and processing information with speed and accuracy far beyond the capabilities of conventional optics and electronics.