Abstract: We discuss deterministic numerical methods such as discrete ordinates methods,spherical harmonic dimensional and iteration acceleration method,for particle (neutron and radiation) transport equations in one-dimensional spheric geometry and twodimesional cylindrical geometry. Recent advances on numerical methods of transport problems are briefly described,including adaptive time step discrete scheme,iterative methods for eigenvalue problems,modified subcell balance methods,simplified spherical harmonic methods,simulation methods for coupling of diffusion and transport,parallel discrete scheme with interface prediction and correction,grey transport synthetic acceleration method,etc. Based on the analysis of difficulties in numerical methods for transport equations,suggestions for future work are proposed.

Key words: particle transport equation, computational method, discrete ordinates method, spherical harmonic methods