Upon femtosecond laser excitation in quantum materials, it is possible to study the many-body interactions through the non-equilibrium processes, realize ultrafast electronic phase transitions, and achieve photoinduced novel states or hidden states. Such studies of the interaction between the ultrafast laser and the quantum materials are the frontiers and attract significant research interests in the field of condensed matter physics. Time- and angle-resolved photoemission spectroscopy is a key experimental tool to study the ultrafast electronic dynamics in quantum materials after photoexcitation. This paper reviews the development of a high-resolution time- and angle-resolved photoemission system based on nonlinear optical crystals and the studies on the ultrafast electronic dynamics in quantum materials using such a setup, including (1) probing the unoccupied electronic states in quantum materials, (2) photoinduced ultrafast electronic phase transitions, and (3) photoinduced new states of matter.