With the rapid development of Internet-driven services, especially the explosive increases of the Internet-based video and peer-to-peer interactive applications, the global IP traffic broke the Zettabyte (ZB) threshold at the end of 2016 and it will grow at a compound annual growth rate (CAGR) of 22 percent from 2015 to 2020. By the end of 2020, global traffic will reach 2.3 ZB per year, or 194.4 EB per month under Cisco’s forecast and methodology (Fig. 1) [1]. As a result, a global community of researchers and engineers is relentlessly striving to improve the backbone and local network infrastructures that can carry more data, more efficiently than ever before. Over the last several decades, optical communication technologies have been advancing rapidly, supporting the ever-growing bandwidth requirements. The transmission capacity of a single optical fiber now is up to 2.15 Pb/s [2]. To increase this figure-of-merit, researchers have been striving to find innovative ways to explore and optimize the physical dimensions of optical light. As shown in Fig. 2, mainly five physical dimensions can be used for modulation and multiplexing to increase the capacity over optical fiber links, i.e. time, wavelength, polarization, space (multicore fiber, linearly polarized (LP) modes, orbital-angular momentum (OAM) and vector modes) and quadrature (phase and amplitude) [2–۱۲]. Obviously, multi-dimension, utilizing more than two dimensions of * Corresponding author. E-mail address: lsyan@swjtu.edu.cn (L. Yan). the light simultaneously to increase the overall capacity, is one of the essential characteristics of next generation optical communication systems. In this paper, we first give a brief overview of recent advances in transmission of multi-dimensional signals for next generation optical communication systems, with an emphasis on optical time-divisionmultiplexing (OTDM), wavelength-division-multiplexing (WDM), spacedivision-multiplexing (SDM), quadrature modulation and polarizationdivision-multiplexing (PDM). In Section 3, we present recent advances of exploring polarization dimension to increase the transmission capacity over standard single-mode-fiber (SMF) links, including nonorthogonal PDM, pseudo-PDM (PPDM) of three and four polarization states (PPDM-3 and -4). In Section 4, before the summary, we will briefly discuss the trends and challenges of multi-dimensional signal transmission technologies.