Inverse modelling techniques have been introduced as a key tool in medical image reconstruction to reconstruct internal anatomical and physiological structures from indirect measurement data from imaging systems. This paper summarizes some of the mathematical background, computational techniques and recent advances in inverse modelling for computed tomography, magnetic resonance imaging, positron emission tomography and ultrasound imaging inverse problems. It introduces forward and inverse imaging model, the difficulties with ill-posed inverse problems and the significance of regularization techniques to stable and exact solutions. Besides, analytical reconstruction methods and deep learning enabled inverse models are comparatively compared for their reconstruction quality, computational efficiency, robustness and clinical applicability. The study demonstrates that the mathematical optimization combined with data-driven learning leads to a substantial improvement of the accuracy of the reconstruction, yet it also diminishes the noise, artifacts, and imaging acquisition time, which can lead to more reliable, efficient, and clinically interpretable medical imaging systems for advanced healthcare applications.