Extremely large antenna array (ELAA) is a common feature of several key candidate technologies for sixth-generation mobile networks (6G), such as ultra-massive multiple-input-multiple-output (UM-MIMO), cell-free massive MIMO, reconfigurable intelligent surface (RIS), and terahertz communications. Since the number of antennas is very large for ELAA, the electromagnetic radiation field needs to be modeled by near-field spherical waves, which is opposed to the conventional planar-wave-based radiation model of 5G massive MIMO. As a result, near-field communications will become essential in 6G wireless networks. In this article, we systematically investigate the emerging near-field communication techniques. Firstly, we present the fundamentals of near-field communications and the metric to determine the near-field ranges in typical communication scenarios. Then, we investigate recent studies specific to near-field communications by classifying them into two categories, i.e., techniques addressing the challenges and those exploiting the potentials in near-field regions. Their principles, recent progress, pros and cons are discussed. More importantly, several open problems and future research directions for near-field communications are pointed out. We believe that this article would inspire more innovations for this important research topic of near-field communications for 6G.