Reconfigurable antennas (RAs), capable of dynamically adapting their radiation patterns, polarization states, and operating frequencies, have emerged as a promising technology to meet the stringent performance requirements of sixth-generation (6G) wireless networks. This article systematically introduces essential hardware implementations of RAs and investigates advanced array architectures, such as fully-digital and tri-hybrid designs, emphasizing their capability to synergistically integrate electromagnetic (EM) reconfigurability with analog and digital signal processing. By facilitating coordinated beamforming across the EM and signal processing domains, RA arrays offer unprecedented flexibility and adaptability compared to conventional static antenna systems. Representative applications empowered by RA arrays, including integrated sensing and communication (ISAC), physical layer security (PLS), and near-field communications, are highlighted. A case study illustrates the effectiveness of RA arrays in optimizing beam steering, improving link robustness, and alleviating system power consumption. Finally, several open challenges and future research directions are outlined, emphasizing the need for advancements in theoretical modeling, hardware reliability, channel estimation techniques, intelligent optimization methods, and innovative network architectures, to fully realize the transformative impact of RAs in future 6G wireless networks.