In coherent optical communication systems, the laser phase noise causes the signal to rotate in the complex plane, so the signal carrier phase estimation and recovery are needed in the receiver. The characteristics of current carrier phase estimation algorithms are compared and researched. The basic principles of two classical algorithms Viterbi&Viterbi and blind phase search(BPS) are introduced, and six phase noise estimation algorithms with two-stages are summarized. The hardware complexity and line width tolerance of the eight carrier phase estimation algorithms are compared, and their performances in 16 QAM system are also evaluated.