The $k$-out-of-$n$ system is a fundamental redundancy model in reliability engineering, playing a critical role in safety-critical domains, such as power transmission, transportation network, communication networks and industrial production lines. This paper provides a systematic review of recent research advances in reliability modeling and maintenance strategy optimization for $k$-out-of-$n$ systems. We first introduce the standard $k$-out-of-$n$ model and its extensions, including multi-state, weighted, consecutive, and network configurations, along with their reliability evaluation methods. We then review maintenance models encompassing time-based, condition-based, and economically orien... More >