Improved magnetic resonance (MR) data sampling, under-sampled image reconstruction, and dipole inversion can be achieved using physics-based deep learning methods. These methods leverage the physical models of MR imaging processes to improve the quality and accuracy of MR images. One approach to improving MR data sampling involves optimizing the k-space under-sampling pattern from fully sampled k-space dataset. A pioneering work is called LOUPE [1] which updates the probabilistic density function used to generate binary k-space sampling patterns, and uses a sigmoid approximation to sample from the learned density function. In addition, physics-based deep learning methods can be used for under-sampled image reconstruction by incorporating the imaging physical models into the deep learning architectures. Pioneering works, such as VarNet [2] and MoDL [3], have incorporated physical models by unrolling iterative reconstruction algorithms with deep learning-based regularizers. Moreover, physics-based deep learning has also improved the ill-posed problem of dipole inversion used to extract tissue susceptibility from magnetic field data. QSMnet [4] and DeepQSM [5] are two pioneering works that have tackled this problem by incorporating physical models either into the training loss function or through simulating the training dataset. This thesis contributes to physics-based deep learning for MRI by: 1) improving LOUPE using a straight-through (ST) estimator and extending the improved LOUPE to multi-echo and multi-contrast scenarios; 2) developing pulse sequence for prospective multi-echo gradient echo under-sampling and customized efficient multi-contrast sampling; 3) designing image reconstruction network architectures aggregating multi-echo and multi-contrast image features; 4) utilizing physical models into the loss function for test time fine-tuning to improve generalization; 5) solving Bayesian posterior estimation of dipole inversion problem using Variational Inference (VI) incorporating physical models.