Diffraction of regular waves by arrays of vertical bottom-mounted circular cylinders is investigated using theoretical, computational, and experimental methods. Experiments in an offshore wave basin are designed to measure free surface elevation η at multiple locations in the vicinity of a multi-column structure subjected to regular waves of frequency 0.449 < ka < 0.524 and steepness 0.122 < kA < 0.261, where k is the wavenumber, a the cylinder radius and A the wave amplitude. Results from regular wave data analysis for first-order amplitudes are compared with those from analytical linear diffraction theory, which is shown to be accurate for predicting incident waves of low steepness. Second- and third-order terms are also estimated from the measured time series, and the effects near a second-order near-trapping frequency are compared to semi-analytical second-order diffraction theory. Linear diffraction theory is shown to be very accurate at predicting the global surface elevation features, even for waves of high steepness. However, violent events and significant nonlinear interactions, including breaking induced by wave scattering, have been observed. Furthermore, second-order near-trapping was observed to affect the magnitude of local free surface oscillations as well as scattered far-field radiation.