This article addresses a synchronization phenomenon between two uncoupled oscillators subject to a common random external signal. Phase reduction is the most powerful technique for analytically studying the synchronization phenomena of oscillators. After briefly introducing the phase reduction theory, we review the theoretical results of the phase reduction analysis for the synchronization induced by a common random signal and show that it is a universal phenomenon that can occur in a variety of oscillators. Then we review recent experimental observation of common-random-signal induced synchronization in semiconductor lasers.