Time-reversal invariance is a very powerful concept in classical and quantum mechanics. However, simple experimental evidence of this concept is difficult to obtain. In the field of acoustic waves, where time reversal invariance also occurs, time-reversal experiments may be achieved simply with large ultrasonic piezoelectric transducer arrays. Time-reversal mirrors (TRMs) are made of such reversible acoustic retina, allowing an incident acoustic field to be sampled, recorded, time-reversed, and re-emitted. Time reversal of acoustic fields allows an optimal approach to focus pulsed ultrasonic waves through inhomogeneous media in the sense that it realizes the matched filter in both the spatial and temporal dimensions to the inhomogeneous propagation transfer function. In the field of acoustics, the ability to work directly in the time domain, with piezoelectric retina, allows pulse echo mode processing in an iterative mode. In multitarget media, such an iterative process converges on the most reflective target. In the case of an extended elastic target, automatic resonances of vibration modes can be achieved. TRMs are also innovative tools in the field of fundamental physics. They may be used to study inverse scattering problems, multiple scattering processes, chaotic scattering as well as scattering by turbulent media. Several experiments illustrating these areas will be presented. Applications of TRMs will also be described and include medical applications (kidney stone destruction and hyperthermia) as well as nondestructive testing of solid media. Experimental results illustrating these applications will be presented.