Nonlinear optical (NLO) crystal is one of the important opt-electrical functional materials that can convert laser frequency and obtain wide band tunable coherent sources, thus it possesses crucial strategic and application value in military and civil fields. On the basis of more than 30 years' efforts, the NLO crystals in visible and near infrared region, including -BaB2O4 LiB3O5 and KTiOPO4, have been basically mature. However, there are still many shortcomings for those NLO crystals used in deep ultraviolet (DUV) and mid/far-infrared (IR) regions, thus putting forward more requirements for high performance crystals. For DUV KBe2BO3F2 (KBBF) crystals, the main shortcomings are the use of toxic BeO raw materials and strong layer growth tendency. Wide transparent region and high second harmonic generation (SHG) effect are also expected in new developed DUV NLO crystals. More importantly, a large enough birefringence is highlighted to satisfy the phase-matchable condition and DUV harmonic generation capacity below 200 nm. On the other hand, the main requirement for mid/far-infrared NLO crystals is to maintain the balance between high laser damage threshold and strong SHG response. Indeed, it is a very difficult task to search for good NLO crystals through the traditional trial and error experimental methods. Theoretical studies, especially first principles calculations, can provide an efficient way to investigate and design new NLO materials with superior properties. In this paper, the recent progress of deep-UV and mid-IR NLO crystals is summarized. In addition, the crucial role of first principles calculations in new material exploration and design is highlighted by introducing several typical new NLO crystals, including defect diamond-like compound AgZnPS4, trigonal alkaline metal fluorooxoborate KB4O6F and alkaline earth fluorooxoborate SrB5O7F3. Moreover, some advanced analysis tools are introduced, such as real space atomic cutting method, SHG-weighted mapping, flexible dipole moment model, and non-bonding atomic orbitals analysis, and used to investigate the structure-property relationship in langasite La3SnGa5O14, metal cyanurate Ca3(C3N3O3)2, vanadium-carbonate K3V(O2)2OCO3, etc. Further, the flow chart of high-throughput first principles calculations of NLO crystal is proposed. According to the known or predicted crystal structure, we can obtain the chemical stability, band gap, NLO coefficient, birefringence and phase-matchable capacity quickly, thus easily judging the research potential of a new NLO material. On the basis of these ideas, a great blueprint for NLO crystal material genome engineering is highly put forward. Finally, the difficulties in research and challenges in NLO material investigations are discussed, and the direction of future research priorities based on first principles calculations are pointed out.