Giant molecular clouds (GMCs) are the primary reservoir of cold molecular gas in the interstellar medium and sites of ongoing star formation. It has been known for decades that star formation efficiency (SFE) of GMCs is very low. While UV radiation feedback from massive stars are expected to play a crucial role in controlling the GMC lifetime and SFE, our theoretical understanding of how it actually works in turbulent, magnetized clouds remains incomplete. In this talk, I will report recent progress we made in modeling GMC destruction by UV radiation feedback. I will first briefly review the predictions made by 1D models about SFE, cloud lifetime, and importance of photoionization and radiation pressure in different star-forming environments. I will then present the results of radiation (magneto)hydrodynamic simulations of star-forming GMCs and discuss how turbulence and magnetic fields can change the picture. If time allows, I will also talk about ongoing efforts in modeling GMC evolution with all major forms of feedback processes (radiation/winds/SNe).