The client library is a critical component of a Redis-powered application, serving as the interface between the software and the Redis server. It performs standardized tasks such as RESP specification conformity, unique language-specific implementation, and connection management. Connection management is a technical point where there's a large variance among different libraries, with three basic schools of thought: unmanaged connections, pooled connections, and multiplexing. Multiplexing allows for fast and efficient handling of multiple threads by sharing a single connection, but it also presents challenges such as client-blocking operations and limitations in functionality. The use of multiplexing can have advantages in terms of latency and pipelining, but it's not always the best choice, especially when dealing with certain Redis operations. Understanding the pros and cons of multiplexing is crucial when choosing a Redis client library.