Antisymmetric magnetic exchange interaction-so-called Dzyaloshinskii-Moriya interaction (DMI)-governs intriguing magnetic phenomena in spintronic materials. A sizeable DMI causes chiral magnetic phenomena such as the formation of chiral magnetic domain walls and the topological magnetic skyrmions. Since the stability and functionality of these chiral objects are largely attributed to the strength of the DMI, an unambiguous determination of the DMI is essential for engineering the chiral spintronic applications. Here, we review recent progresses on the measurement schemes of the DMI strengths and related phenomena.