In this paper, we reviewed our common phase error (CPE) and intercarrier interference (ICI) compensa- tion methods for coherent optical orthogonal frequency division multiplexing (CO-OFDM) system. We first presented a unified CPE estimation framework combining decision-aided (DA), pilot-aided (PA) and decision feed- back (DF) algorithms. The DA method is used to estimate the CPE of the current OFDM symbol based on the decision statistics of the previous symbol. DA + PA helps increase the phase noise tolerance of DA and reduce the overhead of PA, while DA + DF reduces the overhead to zero, achieving best performance with one more step of estimation, compensation and demodulation. We also described a modified time-domain blind intercarrier interference (BL-ICI) mitigation algorithm over non- constant amplitude formats. The new algorithm is derived from the BL-ICI algorithm over constant amplitude format for wireless networks. A new power estimation scheme was proposed for the BL-ICI algorithm to adapt to non- constant amplitude format. It has the same order of complexity with frequency domain decision-aided ICI (DA-ICI) compensation method and does not suffer from symbol decision errors. The effectiveness of both CPE and ICI compensation algorithms were demonstrated in a simulated 56-Gbit/s CO-OFDM system with various modulation formats.