Acoustic waves in liquids are known to have wavelengths comparable to that of visible light if the frequency is in the gigahertz range. The phenomena of Brillouin scattering in liquids is based on such waves. In helium near 2 K acoustic waves with a wavelength of 2000 Å were studied some ten years ago at UCLA. It follows from these observations that an imaging system based on acoustic radiation with a resolving power competitive with the optical microscope is within reach if an ideal lens free from aberrations could be found. Such a lens, which was so elusive at the beginning, is now a simple device and it is the basic component in the acoustic microscope that forms the basis for this review. In this article we will establish the characteristic properties of this new instrument. We will review some of the simple properties of acoustic waves and show how a single spherical surface formed at a solid liquid interface can serve as this ideal lens free from aberrations and capable of producing diffraction limited beams. When this is incorporated into a mechanical scanning system and excited with acoustic frequencies in the microwave range images can be recorded with acoustic wavelengths equal to the wavelength of visible light. We will present images that show the elastic properties of specimens selected from the fields of material science, integrated circuits, and cell biology. The information content in these images will often exceed that of the optical micrographs. In the reflection mode we illuminate the smooth surface of a crystalline material with a highly convergent acoustic beam. The reflected field is perturbed in a unique way that is determined by the elastic properties of the reflecting surface and it shows up in the phase of the reflected acoustic field. There is a distinct and characteristic response at the output when the spacing between the object and the lens is varied. This behavior in the acoustic ieflection microscope provides a rather simple and direct means for monitoring the elastic parameters of a solid surface. It is easy to distinguish between different materials, to determine the layer thickness, and to display variations in the elastic constants on a microscopic scale. These features lead us to believe there is a promising future for the field of acoustic microscopy.