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One of the biggest obstacles in coherent optical communication used to be the synchronization of transmit and local oscillator (LO) laser. Especially for homodyne systems, the need for optical phase-locked loops posed stringed requirements on the line-width of transmit and LO lasers. To overcome these requirements, digital signal processing techniques have been proposed, which can be used to synchronize a free-running LO laser with the received optical signal in the digital domain. Only recently, advances in digital signal processor (DSP) technology allowed for lab demonstration of DSP-aided coherent optical receivers. In this paper, we will review some of the techniques for realizing robust coherent receivers with free-running LO lasers utilizing digital signal processing techniques. We will consider digital as well as analog links.