After 10 years of progress and innovation, optical coherence elastography (OCE) based on the propagation of mechanical waves has become one of the major and the most studied OCE branches, producing a fundamental impact in the quantitative and nondestructive biomechanical characterization of tissues. Preceding previous progress made in ultrasound and magnetic resonance elastography; wave-based OCE has pushed to the limit the advance of three major pillars: (1) implementation of novel wave excitation methods in tissues, (2) understanding new types of mechanical waves in complex boundary conditions by proposing advance analytical and numerical models, and (3) the development of novel estimators capable of retrieving quantitative 2D/3D biomechanical information of tissues. This remarkable progress promoted a major advance in answering basic science questions and the improvement of medical disease diagnosis and treatment monitoring in several types of tissues leading, ultimately, to the first attempts of clinical trials and translational research aiming to have wave-based OCE working in clinical environments. This paper summarizes the fundamental up-to-date principles and categories of wave-based OCE, revises the timeline and the state-of-the-art techniques and applications lying in those categories, and concludes with a discussion on the current challenges and future directions, including clinical translation research.