Diffraction-limited beams were first discovered by Durnin in 1987. These beams are pencil- like and have very large depth of field. Recently, we have discovered new families of diffraction-limited beams which contain some of the diffraction-limited beams known previously, such as, the plane wave and Durnin's Bessel beams, in addition to an infinite variety of new beams, such as X waves. In this paper, we generalize the new diffraction- limited beams to n-dimensional space, review the recent development of the diffraction-limited beams, and describe their applications to medical ultrasonic imaging, tissue characterization and nondestructive evaluation of materials. Advantages and disadvantages of these beams are discussed and their possible applications to other wave related fields are addressed.