Sulfur removal from natural gas, light hydrocarbons, diesel-range fuels, and heavy petroleum fractions is governed not only by intrinsic reaction chemistry but also by adsorption and catalytic surface phenomena, interphase mass transfer, internal diffusion, hydrodynamics, downstream separation, and energy input. This paper develops a diagnostic reaction–transport–separation framework for interpreting desulfurization performance across gas- and liquid-phase systems. Rather than providing an exhaustive review of all desulfurization technologies, representative routes are used to illustrate controlling regimes, including hydrodesulfurization, oxidative desulfurization, catalytic oxidation/sweetening, adsorption/reactive adsorption, and radical-assisted oxidation. Systems are classified as reaction-controlled, external-mass-transfer-limited, internal-diffusion-limited, separation-limited, energy/intensification-limited, or mixed using apparent kinetic constants, volumetric mass-transfer coefficients, effectiveness factors, Thiele moduli, and Damköhler-type ratios. Hydrodynamic cavitation is treated as an intensification layer that may improve interfacial renewal, oxidant activation, and apparent rates only when these benefits exceed energy, erosion, emulsion, and separation penalties. A dimensionless cavitation enhancement factor is proposed to relate apparent rate improvement to measurable cavitation intensity while avoiding double-counting of physical and chemical effects. Illustrative ODS and HDS calculations show how regime analysis prevents overinterpretation of apparent rate constants. The framework provides an engineering basis for selecting hybrid reactors and defining validation requirements for scale-up, including sulfur speciation, closed sulfur balances, independent mass-transfer measurements, catalyst or adsorbent durability, oxidant utilization, and energy-normalized sulfur removal.