The large-sized crystalline materials are the basic raw materials in semiconductors, lasers, and communications. The preparation of large-scale, high-quality crystalline materials has become a bottleneck restricting the development of related industries. Breaking through the preparation theory and technology of large-sized crystal materials is the key to obtaining high-quality large-sized crystals. The preparation process of crystal materials often undergoes the nucleation and growth stages, which also includes multiple processes at the spatiotemporal scale: from atom/ molecules, through clusters and nuclei, final to bulk crystals. To explore and accurately understand the crystal growth mechanism, we firstly make clear the multi-scale process. Thus, it is requires multi-scale in situ characterization techniques and computational simulation methods. Firstly, this paper reviews the latest in situ characterization methods for crystal growth, i.e. optical microscopy, electron microscopy, vibration spectra, synchrotron radiation, neutron technology, and machine learning method. Then, multi-scale computational simulation techniques for crystallization is introduced, for example, first principles calculation at atom/molecular scale, molecular dynamics simulation, Monte Carlo simulation, phase field simulation at mesoscopic scale, and finite element simulation at macroscopic scale. A single in situ characterization or simulation technique can only explore crystallization information over a specific time and space scale. To accurately and fully reflect the crystallization process, a combination of multi-scale methods is required.The establishment of in-situ characterization technology and computational simulation methods for the actual large-sized crystal growth environment will be the future development trend, which provide an important experimental and theoretical basis for developing crystallization theory and controlling crystal quality. The combination of in-situ characterization technology with machine learning and big data technology will be future trend for large-sized crystal growth, which will greatly shorten the R&D cycle.