The subject of multielement ultrasonic transducers is presented, with emphasis on describing the ultrasonic transducer design techniques and time-delay pulsing schedules used to achieve real-time imaging, beam steering, and beam focusing. Transducer design techniques make use of a first-order scattering theory in fluids, which model quite nicely many basic problems in diagnostic ultrasound. The various sidelobe energy and resolution problems are explored as a function of such transducer array design parameters as gapping effects, numbers of elements, ultrasonic excitation waveform shapes and frequencies, element size, and element electronic time-delay pulsing schedules. The electronic time-delay pulsing schedules are responsible for waveform constructive and destructive interference phenomena at points of interest in the ultrasonic field; the time-delay schedules can, therefore, be used to achieve focusing and steering, in both linear array and rectangular array transducer systems. Time-delay analysis and mechanical rotation concepts are used to achieve focusing and steering in annular array transducers. A comparison of the resolution characteristics of annular and linear array transducers is discussed. Axial and lateral resolution as a function of depth and various dynamic focusing concepts are also presented. An introduction to the problems and advantages of rectangular array transducer design is outlined. Sample theoretical and experimental results are presented to highlight the principle concepts associated with the design and utilization of ultrasonic transducer arrays in the medical field.