In recent years, short-reach optical links have attracted much more attention and have come to constitute a key market segment due to the rapid development of data-center applications and cloud services. Four-level pulse amplitude modulation (PAM4) is a promising modulation format to provide both a high data rate and relatively low cost for short-reach optical links. However, the direct detector and low-cost components also pose immense challenges, which are unforeseen in coherent transmission. To compensate for the impairments and to truly meet data rate requirements in a cost-effective manner, various digital signal processing (DSP) technologies have been proposed and investigated for short-reach PAM4 optical links. In this paper, an overview of the latest progress on DSP equalization technologies is provided for short-reach optical links based on PAM4 modulation. We not only introduce the configuration and challenges of the transmission system, but also cover the principles and performance of different equalizers and some improved methods. Moreover, machine learning algorithms are discussed as well to mitigate the nonlinear distortion for next-generation short-reach PAM4 links. Finally, a summary of various equalization technologies is illustrated and our perspective for the future trend is given. Appl. Sci. 2019, 9, 2342 2 of 22 multi-tone (DMT), and quadrature amplitude modulation (QAM) based on Kramers-Kronig (KK) receiver [18]. Considering the power consumption and implementation complexity, the most attractive format in short-reach optical links is PAM4, which is believed as a highly promising candidate for the next-generation passive optical network (NG-PON) and has been ratified by IEEE 802.3 bs for 400 Gbps Ethernet transmission [19][20][21][22][23][24][25].However, the low-pass filtering effects induced by the limited bandwidth of transmitter and receiver can cause severely inter-symbol interference (ISI). Low-cost devices such as lasers, modulators, photodiodes (PD) and trans-impedance amplifiers (TIA) also produce nonlinear distortions like level-dependent skew and level-dependent noise. Furthermore, the interaction between chromatic dispersion (CD) and direct detection will lead to a power-fading effect, where the detected signal may contain frequency notches after several kilometers transmission at a high symbol rate. Therefore, various equalization technologies based on digital signal processing (DSP) have been investigated for short-reach links over the years . Conventional equalizers, such as the feed-forward equalizer (FFE) or decision feedback equalizer (DFE), are employed to compensate for the linear impairments induced by limited bandwidth and CD [26][27][28], while the equalizer based on the Volterra series is utilized to mitigate nonlinear distortion [29][30][31][32]. Some new equalization techniques, such as direct detection-faster than Nyquist (DD-FTN) algorithm [33][34][35], intensity directed FFE/DFE (ID-FFE/ID-DFE) algorithm [36,37] and joint clock recovery and FFE (CR-FFE) algorithm...