## 1 Introduction  
Driven by upcoming services such as the Internet of Things (IoT), 4K/8K video applications, virtual reality (VR) and big data, the global internet protocol (IP) traffic has grown explosively in recent years [1]. As predicted by a Cisco report [2], 4.8 zettabytes of annual global IP traffic will be reached by 2022 and the so-called \"Zettabbyte Era\" has arrived. To accommodate the associated demands, short-reach optical links have been widely investigated for data center interconnects (DCI), metro network, optical access, and so forth [3]. Unlike long-reach transmission, the short-reach optical links are especially sensitive to cost and size due to the large scale of their deployment [4]. Therefore, intensity modulation with direct detection (IM/DD) is adopted as the mainstream solution instead of coherent detection [5; 6; 7]. Traditional IM/DD optical interconnects implemented with non-return-to-zero on-off-keying (NRZ-OOK) format struggle to support the requirements of the increased transmission rate. Thus, many advanced modulation formats are employed to improve the spectrum efficiency (SE) and reduce the bandwidth limitation for electronic and optical components [8; 9; 10; 11; 12; 13; 14; 15; 16; 17], such as four-level pulse amplitude modulation (PAM4), carrier-less amplitude and phase modulation (CAP), discrete 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 [26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53]. 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 [38; 39], have recently been proposed to solve different problems in practical implementation. In addition, machine learning methods like support vector machine (SVM) [40; 41; 42] and neural network (NN) [43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53] have been investigated to further eliminate system impairments for PAM4 modulation. In this paper, an overview is provided on the important topic of advanced DSP for short-reach PAM4 optical links. The rest of this paper is organized as follows. In Section 2, the system configuration is introduced for short-reach PAM4 transmission in detail, where the comparisons for different transmitters and receivers are presented as well. Section 3 describes the distortions of high-speed transmission with low cost, including limited bandwidth, CD, nonlinear devices and power fading effect.