We present our recent theoretical and numerical studies concerning the properties of cholesteric blue phases (BPs). One is on the effect of the variation of the Frank elastic constants on the stability of BPs. Our study is based on a classical and well-known theory of Meiboom et al. that gave a rough estimate of the temperature range of stable BPs in the case of equal elastic constants. We extend it to take into account the difference of the elastic constants. We show that the stability of BPs is greatly enhanced when the bend elastic constant K33 is smaller, which agrees well with recent experiments. We also show that larger splay (K11) and twist (K 22) elastic constants are also favorable for the stability of BPs. The other subject of the present paper is the response of BPs in a parallel cell to an applied electric field. We carry out numerical calculations for the investigation the dynamics of orientational order and associated disclination lines. Our calculations are based on a Landau-de Gennes theory describing the orientational order of the liquid crystal by a second-rank tensor. Our preliminary calculations demonstrate that a non-uniform electric field induced by comb-like electrodes gives rise to non-trivial dynamics of disclination lines.