Magnetic resonance fingerprinting (MRF) is a brand new MRI technology that features fast, quantitative, and simultaneous mapping of multiple MR and tissue properties, such as proton density, relaxation times and diffusion coefficients. In data acquisition, MRF employs a series of pseudo-randomized RF flip angles and repetition times to excite the spin system for a series of undersampled spatial images, forming a temporal MR signal evolution curves (named measured fingerprints) for each image voxel; on the other hand, a set of signal evolution curves are acquired theoretically by computer simulation and Bloch equation, with all foreseeable combination of tissue parameters (such as T 1, T 2, Proton density, etc) and using the same RF and TR series as in the real MR scan. All the calculated signals and their corresponding parameters constitute a database of fingerprints termed a dictionary. In image reconstruction, the measured fingerprints (i.e., the temporal evolutions of individual voxels of the undersampled images) are compared with the entries in the dictionary (i.e., the simulated theoretical signal evolutions with all possible tissue parameters), using pattern recognition and/or data mining, for the best matches; the tissue parameters corresponding to the best matched dictionary entry are determined for the corresponding voxels. Finally, the collection of these parameters are presented as parametric images, such as T 1-map, T 2-map, and PD-map, instead of T 1-weighted, T 2-weighted, or PD-weighted images. MRF technology breaks the limitation of the conventional, qualitative, motion-sensitive, and time-consuming MRI techniques. It also makes possible the sub-voxel parametric mapping. The multiparametric and quantitative features of MRF are in conformity with and will have great impact on modern model of precision and personalized medicine. This paper introduces the basic principles of MRF, provides detailed description and analysis for RF/TR series optimization, dictionary design, and signal reconstruction, and presents latest development in both the MRF technique and its application in biomedical research. We also discuss the challenges and future directions for MRF research and applications.