Pinching antennas have emerged as a promising technology for reconfiguring wireless propagation environments, particularly in high-frequency communication systems operating in the millimeter-wave and terahertz bands. By enabling dynamic activation at arbitrary positions along a dielectric waveguide, pinching antennas offer unprecedented channel reconfigurability and the ability to provide line-of-sight (LoS) links in scenarios with severe LoS blockages. The performance of pinching-antenna systems is highly dependent on the optimized placement of the pinching antennas, which must be jointly considered with traditional resource allocation (RA) variables -- including transmission power, time slots, and subcarriers. The resulting joint RA problems are typically non-convex with complex variable coupling, necessitating sophisticated optimization techniques. This article provides a comprehensive survey of existing RA algorithms designed for pinching-antenna systems, supported by numerical case studies that demonstrate their potential performance gains. Key challenges and open research problems are also identified to guide future developments in this emerging field.