Optical coherence elastography (OCE), as the use of OCT to perform elastography has come to be known, began in 1998, around ten years after the rest of the field of elastography – the use of imaging to deduce mechanical properties of tissues. After a slow start, the maturation of OCT technology in the early to mid 2000s has underpinned a recent acceleration in the field. With more than 20 papers published in 2015, and more than 25 in 2016, OCE is growing fast, but still small compared to the companion fields of cell mechanics research methods, and medical elastography. In this review, we describe the early developments in OCE, and the factors that led to the current acceleration. Much of our attention is on the key recent advances, with a strong emphasis on future prospects, which are exceptionally bright.