In this paper, we reviewed our common phase error (CPE) and intercarrier interference (ICI) compensation 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 feedback (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 nonconstant 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 nonconstant 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.