Efficient electrical control of magnetism is an important requirement for future spintronic devices. In this regard, current-induced magnetization dynamics at room temperature has received considerable attention in the last decade and some of leading companies in semiconductor industry are developing spintronic devices such as spin-transfer-torque magnetic RAM based on this particular phenomenon. In this talk, I will first review some of recent experiments addressing effects of spin-orbit coupling on the current-induced magnetization dynamics. Performed mostly for magnetic bilayer structures, which consist of a ferromagnetic layer (Co, Fe etc) and a heavy metal (Pt, Ta, W) or topological insulator layer, these experiments show that the spin-orbit coupling drastically modify the current-induced magnetization dynamics and makes possible what was thought to be impossible. I will then present ongoing theoretical efforts to understand the spin-orbit coupling effects. While rough qualitative understanding is possible through three well-known effects of spin-orbit coupling (spin Hall effect, Dzyaloshinskii-Moriya interaction, and Rashba-type interfacial spin-orbit interaction), their nature in the magnetic bilayers and their roles on the current-induced magnetization dynamics yet remain controversial. I will briefly introduce these controversies and present more recent theoretical ideas, if time allows.