Digital Inline Holographic Microscopy (DIHM) has emerged as a powerful and cost-effective imaging technique for microscopy, enabling the acquisition and numerical reconstruction of threedimensional information from two-dimensional holograms. A central challenge in DIHM is the phase retrieval problem, which is fundamental for accurate image reconstruction and autofocusing. This paper presents a comprehensive review of numerical diffraction and phase retrieval methods applied to inline digital holography, with emphasis on their theoretical foundations, computational characteristics, and practical implementation. The analyzed approaches are organized into three main categories: direct methods, which numerically solve diffraction integrals using approximations such as Fresnel and Angular Spectrum formulations; iterative methods, including the Gerchberg–Saxton algorithm and its extensions proposed by Fienup; and data-driven methods based on deep learning, which leverage convolutional neural networks to infer phase information directly from holograms. Additionally, classical and learning-based autofocusing strategies are discussed, highlighting criteria based on image sharpness, statistical measures, and neural regression.