Atmospheric particles, i.e. ice crystals, dust particles, and black carbon, show significant complexities like irregular geometries, inhomogeneity, small-scale surface structures, and play a significant role in the atmosphere by scattering and absorbing the incident solar radiation and terrestrial thermal emission. Knowledge of aerosol scattering properties is a fundamental but challenging aspect of radiative transfer studies and remote sensing applications. This dissertation tries to improve our understanding on the scattering properties of atmospheric particles by investigating both the scattering algorithms and the representation of the realistic particles. One part of this dissertation discusses in details the pseudo-spectral time domain algorithm (PSTD) for calculating scattering properties, its advantages and the elimination of the Gibbs phenomenon. The applicability of the parallelized PSTD implementation is investigated for both spherical and nonspherical particles over a wide range of sizes and refractive indices, and the PSTD is applied for spherical particles with size parameters up to 200, and randomly oriented non-spherical ones with size parameters up to 100. The relative strengths of the PSTD are also shown by a systematic comparison with the discrete dipole approximation (DDA). The PSTD outperforms the DDA for particles with refractive indices larger than 1.4, and ones with smaller refractive indices by large sizes (e.g. size parameters larger than 60 for a refractive index of 1.2). The results suggest significant potential of the PSTD for the numerical investigation of the light scattering and corresponding atmospheric applications. The other part of this dissertation investigates the effects of particle complexities on the light scattering properties of the atmospheric particles, and three aspects corresponding to the irregular geometry, inhomogeneity and surface roughness are studied. To cover the entire particle size range from the Rayleigh to the geometric- optics regimes, the PSTD (for relatively small particles) is combined with the im- proved geometric-optics method (IGOM) that is only applicable for large particles. The Koch-fractal geometry is introduced to model the light scattering properties of aerosol, and performs an excellent job of reproducing the experimental measurements of various mineral dust particles. For the inhomogeneous particles, the applicability of the effective medium approximations (EMA) is tested, and the EMA can be used to approximate the scattering properties of inhomogeneous particles only when the particles are uniformly internal mixtures. Furthermore, an irregular rough model is developed to study the effects of the small-scale surface roughness on the light scattering properties. In conclusion, the dissertation finds that the complexities of atmospheric particles have to be fully considered to obtain their scattering properties accurately.