This dissertation investigates the use of advanced acoustical communication techniques for wireless downhole telemetry systems. Using acoustic waves for downhole telemetry systems is investigated in order to replace the wired communication systems currently being used in oil and gas wells. While the acoustic technology offers great benefits, a clear understanding of its propagation aspects inside the wells is lacking. This dissertation describes a testbed that was designed to study the propagation of acoustic waves over production pipes. The wireless communication system was built using an acoustic transmitter, five connected segments of seven inch production pipes, and an acoustic receiver. The propagation experiments that were conducted on this testbed in order to characterize the channel behavior are explained as well. Moreover, the large scale statistics of the acoustic waves along the pipe string are described. Results of this work indicate that acoustic waves experience a frequency- dependent attenuation and dispersion over the pipe string. In addition, the testbed was modified by encasing one pipe segment in concrete in order to study the effect of concrete on wave propagation. The concrete was found to filter out many of the signal harmonics; accordingly, the acoustic waves experienced extra attenuation and dispersion. Signal processing techniques are also investigated to address the effects of multipaths and attenuation in the acoustic channel; results show great enhancements in signal qualities and the usefulness of these algorithms for downhole communication systems. Furthermore, to explore an alternative to vibrating the body of a cemented pipe string, a testbed was designed to investigate the propagation aspects of sound waves inside the interior of the production pipes. Results indicate that some low-frequency sound waves can travel for thousands of feet inside a cemented pipe string and can still be detected reliably.