Extremely large-scale arrays (XL-arrays) have emerged as a promising technology to achieve super-high spectral efficiency and spatial resolution in future wireless systems. The large aperture of XL-arrays means that spherical rather than planar wavefronts must be considered, and a paradigm shift from far-field to near-field communications is necessary. Unlike existing works that have mainly considered far-field beam management, we study the new near-field beam management for XL-arrays. We first provide an overview of near-field communications and introduce various applications of XL-arrays in both outdoor and indoor scenarios. Then, three typical near-field beam management methods for XL-arrays are discussed: near-field beam training, beam tracking, and beam scheduling. We point out their main design issues and propose promising solutions to address them. Moreover, other important directions in near-field communications are also highlighted to motivate future research.