Soil amendments play a critical role in improving soil health and supporting sustainable crop production, especially under declining soil fertility and climate-related stress. However, their impact varies because each amendment influences the soil through different biogeochemical processes rather than a single universal mechanism. This review synthesizes current knowledge on a wide range of soil amendments, including compost, biosolids, green and animal manure, biochar, hydrochar, bagasse, humic substances, algae extracts, chitosan, and newer engineered options such as metal–organic framework (MOF) composites, highlighting their underlying principles, modes of action, and contributions to soil function, crop productivity, and soil carbon dynamics. Across the literature, three main themes emerge: improvement of soil physicochemical properties, enhancement of nutrient cycling and nutrient-use efficiency, and reinforcement of plant resilience to biotic and abiotic stresses. Organic nutrient-based amendments mainly enrich the soil and build organic matter, influencing soil carbon inputs and short- to medium-term increases in soil organic carbon stocks. Biochar, hydrochar, and related materials act mainly as soil conditioners that improve structure, water retention, and soil function. Biostimulant-type amendments, such as algae extracts and chitosan, influence plant physiological responses and stress tolerance. Humic substances exhibit multifunctional effects at the soil–root interface, contributing to improved nutrient efficiency and, in some systems, enhanced carbon retention. The review highlights that no single amendment is universally superior, with outcomes governed by soil–crop context. Its novelty lies in its mechanism-based, cross-amendment synthesis that frames both yield and carbon outcomes as context-dependent rather than universally transferable. Within this framework, humic substances and carbon-rich materials show potential for climate-smart soil management, but long-term carbon sequestration effects remain uncertain and context-dependent.