The Sun-Earth Lagrange point L4, which is called a parking space of space, is considered one of the unique places where solar activity and the heliospheric environment can be observed continuously and comprehensively. The L4 mission affords a clear and wide-angle view of the Sun-Earth line for the study of Sun-Earth connections from remote-sensing observations. The L4 mission will significantly contribute to advancing heliophysics science, improving space weather forecasting capability, extending space weather studies far beyond near-Earth space, and reducing risk from solar radiation hazards on human missions to the Moon and Mars. Our paper outlines the importance of L4 observations by using remote-sensing instruments and advocates comprehensive and coordinated observations of the heliosphere at multi-points including other planned L1 and L5 missions. We mainly discuss scientific perspectives on three topics in view of remote sensing observations: (1) solar magnetic field structure and evolution, (2) source regions of geoeffective solar energetic particles (SEPs), and (3) stereoscopic views of solar corona and coronal mass ejections (CMEs).