The free-electron lasers (FELs), a rapid developing technology as a new generation of advanced radiation sources in the last decade, provide ultra-fast, ultra-intense, ultra-short wavelength laser pulses, becoming a robust metrology to explore the forefront of light-matter interactions. In atomic, molecular and optical (AMO) physics, shortwavelength FELs manifest their benefits in exploring multi-photon nonlinear phenomena, observing and controlling reaction dynamics of electrons, atoms and molecules. Experimental advancements from simple helium atom to complex bio-molecules, from outer-shell to inner-shell electrons, from single-photon to multi-photon processes, from single pulse experiments to time-resolved pump-probe approaches, from extreme ultraviolet to hard X-ray regimes, from energy spectra to time-resolved momentum spectra, have successively achieved, all of which are accessible to observe and manipulate quantum world in aspatial scale of atoms and a temporal resolution of femtosecond. The review selects very recent illustrative experimental results in this field and presents the groundbreaking achievements in intriguing quantum behaviors of electrons, atoms and molecules under intense shortwavelength FEL field, demonstrating the fundamental aspects of AMO physics.