In the last few years, there has been significant progress toward designing new types of transmitter arrays for acoustic and electromagnetic radiation. The radiation from these arrays would propagate without spreading and without diminishing in intensity for greater distances than previously was possible. A promising approach to the design of such arrays is through a new class of three-dimensional solutions of the relevant wave equations, which have been named acoustic Bessel bullets. These arrays could have wide-ranging applications in such fields as radar, sonar, biomedical ultrasonics, and nondestructive testing.