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A comprehensive literature review was performed on liver intravoxel incoherent motion (IVIM) magnetic resonance imaging (MRI) technique and its applications. Heterogeneous data have been reported. IVIM parameters are magnetic field strength dependent to a mild extent. A lower Dslow (D) value at 3 T than at 1.5 T and higher perfusion fraction (PF) value at 3 T than at 1.5 T were noted. An increased number of b values are associated with increased IVIM parameter measurement accuracy. With the current status of art, IVIM technique is not yet capable of detecting early stage liver fibrosis and diagnosing liver fibrosis grades, nor can it differentiate liver tumors. Though IVIM parameters show promise for tumor treatment monitoring, till now how PF and Dfast (D*) add diagnostic value to Dslow or apparent diffusion coefficient (ADC) remains unclear. This paper shows the state-of-art IVIM MR technique is still not able …