It has been proved that the physical anisotropies of earth medium, such as resistivity, electric susceptibility, velocity, and quality factor, et al., exist and can't be ignored. For this reason, researches on anisotropy began tens of years ago and now become a hotspot in the field of seismology and geo-electromagnetism in recent years. Promoted by development of information sciences and technology, especially driven by technological progresses of sensor, storage and communication of big dataset, the observations of geophysical field have been upgraded to 2-and 3-dimensional, multi-component vector and tensor measurements at different elevations and spatial sizes, such as 6-component seismic and 5-component MT acquisition provided the possibilities of anisotropic inversion and more precise prediction on physical parameters in geosciences. However, serious challenges have been faced by the traditional geophysics, just because the theoretical principles, methods and techniques of geophysics were built on the basis of scalar observation, and massive vector data are observed and their sharing and utilization become an incontrovertible trend. Thus, in this No.567 Xiangshan-Science Conferences, the progresses and problems in the study of anisotropic geophysics and vector field were introduced and analyzed according to 4 sections. First, different scale and types of vibrations from 6-component earthquake, 3-component seismic exploration and micro-seismic monitoring, and the relations in between are presented and discussed. Secondly, numerical simulations and inversions of resistivity anisotropy are given more discussions; especially on the non-uniqueness of anisotropic inversions for apparent resistivity, tensor observation and azimuthal acquisition were also addressed. Thirdly, the joint geophysical measurements from different altitudes, including well logging, underground geophysical prospecting, airborne and satellite geophysical observations are expected to be used on land, in the ocean and in the air. Finally, instruments of vector seismic sensing and tensor MT and CSAMT, processing techniques of vector signals and software system, communication and storage of big geophysical datasets, including advanced technologies on compressed sensing, were introduced respectively. All these presentations could not be covered in detail within one paper, though, the basic scientific and technological problems about computational geophysics, active or passive seismology, and anisotropic electromagnetism will be focused on, while the detailed discussions on different geophysical fields will follow in other papers, so that the issues on the fundaments and generality of anisotropic geophysics could be studied extensively in the future.