The transition to next-generation mobile communication networks, particularly 6G, demands advanced technologies to meet the requirements for ultra-reliable, low-latency communication, massive connectivity, and intelligent applications. Reconfigurable antennas (RAs) play a crucial role in achieving these objectives by enabling dynamic adjustments to the radio frequency (RF) characteristics of antennas, such as gain, radiation pattern, impedance, and polarization. Unlike traditional fixed-position antennas, RAs can alter both their radiation patterns and positions, offering flexibility in response to varying communication environments. This paper presents a comprehensive survey and tutorial on RAs, with a focus on fluid antennas (FAs), movable antennas (MAs), pinching antennas (PAs), and reconfigurable holographic antennas (RHAs), examining their potential in next-generation mobile networks. We explore the channel modelling and estimation, performance analysis, resource allocation strategies, and their synergy with other emerging wireless technologies for each type of RA. Finally, we provide a comparative analysis of different RAs and discuss the open challenges and future research directions, offering insights and guidance for future investigations in the exciting research area.