We present results and a method to geophysically image the subsurface structures of maar volcanoes to better understand eruption mechanisms and risks associated with maar-forming eruptions. High-resolution ground gravity and magnetic data were acquired across several maar volcanoes within the Newer Volcanics Province of southeastern Australia, including the Ecklin maar, Red Rock Volcanic Complex, and Mount Leura Volcanic Complex. The depth and geometry of subsurface volcanic structures were determined by interpretation of gridded geophysical data and constrained 2.5-D forward and 3-D inverse modeling techniques. Bouguer gravity lows identified across the volcanic craters reflect lower density lake sediments and pyroclastic debris infilling the underlying maar-diatremes. These anomalies were reproduced during modeling by shallow coalesced diatremes. Short-wavelength positive gravity and magnetic anomalies identified within the center of the craters suggest complex internal structures. Modeling identified feeder vents, consisting of higher proportions of volcanic debris, intrusive dikes, and ponded magma. Because potential field models are nonunique, sensitivity analyses were undertaken to understand where uncertainty lies in the interpretations, and how the models may vary between the bounds of the constraints. Rather than producing a single "ideal" model, multiple models consistent with available geologic information are created using different inversion techniques. The modeling technique we present focuses on maar volcanoes, but there are wider implications for imaging the subsurface of other volcanic systems such as kimberlite pipes, scoria cones, tuff rings, and calderas.