Acoustic array signal processing in the ocean faces challenges due to multipath propagation, scattering from objects or surfaces, geometric uncertainty, and limitations from array geometry - all of which can harm conventional beamforming outputs. Frequency-difference and frequency-sum beamforming are out-of-band signal processing techniques that exploit signal bandwidth to beamform at below- or above-band frequencies. The work described here evaluates frequency-difference beamforming's ability to reduce the undesirable effects associated with array sparseness, strong random scattering, or geometric uncertainty, and examines the array coherence properties of both techniques. Frequency-difference beamforming has also been used with Synthetic Time Reversal (STR) for blind deconvolution, and is extended to underwater communications here. The performance of frequency-difference beamforming is evaluated using simulations and experiments in a laboratory water tank and a shallow-ocean environment (KAM11 experiment). The method is shown to mitigate the effects of array sparseness, with results comparable to conventional beamforming when the in-band frequency matches the difference frequency, Δf, despite frequency-difference beamforming using a higher frequency signal. Shallow ocean results show agreement when comparing expected directions-of-arrival (DOAs) and the frequency-difference DOAs, with a reduced-chi-squared of 0.91 in experiments, despite notable multipath and array element spacing of 27-80 in-band wavelengths. Horizontal array simulations indicate that frequency-difference beamforming is robust to random variation in ray-path arrival times when Δf*σ = 0.20 (σ = arrival time standard deviation). Additional water tank simulations and experiments show that frequency-difference beamforming mitigates strong scattering effects by utilizing frequencies where Δka is small (k = wavenumber, a = spherical scatterer radius). Here, frequency-difference beamforming localizes a source with a factor of 4 reduction in error and 5 dB peak-to-sidelobe ratio improvement compared to conventional in-band techniques using the same signals. The coherence lengths of frequency-difference and -sum autoproducts are considered using recordings of a bottom-reflected path with an 8 km towed array (COAST 2012 experiment), showing coherence extending below and above the signal band. Here, averaged coherence lengths were 7.0λ for conventional fields from 1-200 Hz, 12.4λ for frequency-difference autoproducts from 1-100 Hz, and 8.6λ for frequency-sum autoproducts from 40-400 Hz (both using a 10-200 Hz signal band). Blind deconvolution of a communication signal (from KAM11 data) is considered using an Overlapping STR (OSTR) technique that provides real-time channel updates. OSTR is shown to be useful for long-duration signals in time-varying environments and is compared to a standard Time Reversal (TR) method. Here, the TR method yields a bit error rate (BER) = 0.34% and an SNR = 8.5 dB (average bit error in the complex plane). For the same signal, OSTR yields BER = 0.0% and SNR = 12.2 dB. An additional experiment considers acoustic measurements of aeroacoustic noise in a wind tunnel. Conventional beamforming and the Spectral Estimation Method with cross spectral density matrix (CSDM) subtraction, and Robust Principal Component Analysis with a subspace denoising technique are considered for noise removal using a reference measurement. In a ≤ -15 dB SNR environment, localization and source level estimation of field changes are possible when the source level is louder than noise …