Optoacoustic (OA, photoacoustic) imaging capitalizes on the low scattering of ultrasound within biological tissues to provide optical absorption-based contrast with high resolution at depths not reachable with optical microscopy. For deep tissue imaging applications, OA image formation commonly relies on acoustic inversion of time-resolved tomographic data. The excitation of OA responses and subsequent propagation of ultrasound waves can be mathematically described as a forward model enabling image reconstruction via algebraic inversion. These model-based reconstruction methods have been shown to outperform alternative inversion approaches and can further render OA images from incomplete datasets, strongly distorted signals or other suboptimally recorded data. Herein, we provide a general perspective on model-based OA reconstruction methods, review recent progress, and discuss the performance of the different algorithms under practical imaging scenarios.