Electromagnetic scattering by particles is a field of active research with high relevance for such diverse fields as atmospheric science, oceanography, astronomy, and engineering sciences, with specific applications in remote sensing, ecological environment, ocean optics, climate research, scattering by interplanetary dust grains, bio-optical imaging, antenna theory, particle sizing technology, and coating technology. Since its importance, complexity and difficulty, light scattering by nonspherical particles has become an international focus and frontiers of light scattering research and made a lot of studies. In the paper, some basic and important problems on light scattering calculations by nonspherical particles are briefly discussed and summarized. Based on the theoretical foundation of light scattering, the limitations of LorenzMie theory of spherical particles which have been widely used since the 1950 s are pointed out first. From the nature of the impact of nonsphericity of particles on scattering model, the nonequivalence of both the LorenzMie scattering by spherical particles and the light scattering by nonspherical particles is further discussed. Then, the research progresses of modern light scattering calculations by nonspherical particles are expounded and discussed, including accurate theoretical methods, some important numerical methods and two approximation algorithms, namely the approximations by optically soft particles and geometric optics approximation. We also point out that in order to express the light scattering characteristics by quasilayered and more complex particles in nature, the layered particle model and EBCM（Extended Boundary Condition Method）are becoming a hot research field in recent years, which are two noteworthy development trends. Finally, the challenge of the research on light scattering calculation methods by nonspherical particles and the future developments are briefly discussed.