Silicon photonics is considered as a promising technology to overcome the difficulties of the existing digital and analog optical communication systems, such as low integration, high cost, and high power consumption. Silicon optical modulator, as a component to transfer data from electronic domain to optical one, has attracted extensive attentions in the past decade. In this paper, we review the statuses of the silicon optical modulators for digital and analog optical communications and introduce our efforts on these topics. We analyze the relationship between the performance and the structural parameters of the silicon optical modulator and present how to optimize its performance including electro-optical bandwidth, modulation efficiency, optical bandwidth and insertion loss. The fabricated silicon optical modulator has an electro-optical bandwidth of 30 GHz. Its extinction ratios are 14.0 dB, 11.2 dB and 9.0 dB at the speeds of 40 Gbps, 50 Gbps and 64 Gbps for OOK modulation. The high extinction ratio of the silicon optical modulator at the high speed makes it very appropriate for the application of optical coherent modulation, such as QPSK and 16-QAM. The fabricated silicon optical modulator also can be utilized for analog optical communication. With respect to a noise floor of -165 dBc, the dynamic ranges for the second-order harmonic and the third-order intermodulation distortion are 90.8 dB and 110.5 dB respectively. By adopting a differential driving structure, the dynamic range for the second-order harmonic can be further improved to 100.0 dB while the third-order intermodulation distortion remains the same level.