Giant molecular clouds (GMCs) are the primary sites of star formation and stellar feedback in galaxies. UV radiation emitted by newborn massive stars is believed to play a key role in destroying GMCs and limiting star formation efficiency (SFE) therein, but the details of how remain elusive. In this talk, I will report on recent progress we made in modeling of star-forming GMCs with UV radiation feedback. I will overview observational constraints on the GMC lifecycle and present results of radiation (M)HD simulations, focusing on the effects of turbulence and magnetic fields. I will also briefly discuss (1) the escape of ionizing radiation and implications for diffuse ionized gas; and (2) why it is difficult to observationally validate the anti-correlation between turbulence level and star formation rate predicted by theory. I will end by talking about ongoing efforts in modeling GMC destruction with all major forms of massive star feedback (UV radiation, winds, and supernovae).