Garbage collection algorithms are techniques used in programming languages to automatically manage memory. They identify and reclaim memory that is no longer in use, preventing memory leaks and optimizing resource usage. Common algorithms include Mark-and-Sweep, Reference Counting, and Generational Garbage Collection. These algorithms work by tracking objects in memory and determining which ones are still accessible or needed. When an object is no longer referenced, the garbage collector can free up that memory for future use. This process helps maintain system performance and stability, especially in long-running applications.