Modular Multilevel Cascade Converters (MMCCs) are considered a promising power electronics topology in industry. Their scalability allows to reach (ultra/very) high voltage levels with low harmonic content and high efficiency and makes MMCCs an ideal solution for high-power applications; such as electrical drives, solid-state transformers and high-voltage direct-current (HVDC) transmission systems. However, the high levels of thermal, electrical and mechanical stress on the power electronics devices and the large number of components (e.g. capacitors or semiconductors) make MMCCs prone to several kinds of faults. Fault detection and diagnosis (FDD) in combination with fault isolation and system reconfiguration techniques, based on cell redundancy, can increase the reliability, availability and safety of MMCCs, which is crucial for their utilization in critical energy applications. This paper comprehensive surveys: (i) reliability including failure rates, fault modes, failure mechanisms and fault impact analysis, (ii) concepts of fault tolerance and FDD (e.g. expert system, model- or hardware and data-based FDD methods) and (iii) system reconfiguration strategies (e.g. cold- or hot-redundant) for MMCCs. All discussed aspects are related to generic MMCC models and operation principles, unifying notation of over 250 papers and, therefore, simplifying the understanding and comparability. The state-of-the-art, challenges and future research trends and opportunities towards reliable MMCC-based systems are thoroughly collected.