In the past decade, optical diffraction tomography has gained a lot of attention for its ability to create label-free three-dimensional (3D) images of the refractive index distribution of biological samples using scattered fields measured through holography from multiple angles. Although many experimental and computational methods have been conducted to produce decent 3D refractive index tomograms, some theoretical aspects of this technique have not been studied thoroughly, limiting its use to imaging the linear refractive index of a single or a few isotropic cells in homogeneous background. In the techniques proposed so far, the intensity and phase of the scattered field are exploited to reconstruct a 3D sample. However, polarization, as an important feature of light, is not discussed in optical diffraction tomography in order to image anisotropic samples. Nevertheless, many biological samples, especially those with fibrous structures, such as skin or muscle tissues have intrinsic or form birefringence. As a result, polarization-sensitive optical diffraction tomography can provide a 3D reconstruction of novel modalities showing interesting features in the sample which can not be observed in the scalar refractive index distribution. Similarly, samples containing nonlinear optical susceptibility can generate light in other frequencies such as harmonic generation. The nonlinear optical susceptibility can reveal features that are not observable in the linear refractive index distribution. For biological examples, fibrous proteins such as myosin or collagen possess second-order nonlinear optical susceptibility and can show second-harmonic or sum frequency generation. However, the generalization of the optical diffraction tomography approaches to nonlinear processes is not studied yet. A similar approach to optical diffraction tomography can be presented by inversion of the nonlinear wave equations governing the frequency mixing processes and reconstructing the 3D distribution of the nonlinear susceptibility using 2D complex images of the generated frequencies. In this thesis, I generalize conventional optical diffraction tomography to polarization-sensitive and nonlinear media. The proposed methods in this thesis provide novel modalities for optical diffraction tomography which can be used for 3D imaging of anisotropic and nonlinear samples. I present numerical and experimental results for various examples to investigate the viability of the proposed modalities. Another aspect of this thesis is to present an iterative solution for optical diffraction tomography based on a forward model which is as accurate as full-wave electromagnetics simulation and can include different scenarios, such as depolarization, anisotropicity, and nonlinearity. As full-wave solutions cannot be easily used in the gradient-based iterative optimization approaches for optical diffraction tomography, a physics-informed neural network is presented and used as the forward model in an iterative reconstruction of optical diffraction tomography. The methods that are studied in this thesis have a significant impact on optical diffraction tomography and 3D imaging. Through an in-depth theoretical, numerical, and experimental analysis, this research aims to investigate the possibilities of utilizing these techniques in the development of label-free 3D imaging modalities.