As engineering systems grow in scale and complexity, the classical consecutive k-out-of-n model has evolved significantly to address the challenges of component dependence and dynamic maintenance. This paper presents a comprehensive survey of these advancements, categorized into model extensions and assessment methodologies. We synthesize key variants adapted for practical scenarios, including consecutive k-within-m-out-of-n systems, m-consecutive-k-out-of-n systems, (n, f, k) and ⟨n, f, k⟩ systems, sparse $d$ systems, and complex models accounting for component dependence and repair mechanisms. Regarding reliability assessment, this paper evaluates the transition from analytical methods... More >