Mitochondria are small cellular constituents that generate cellular energy (ATP) by oxidative phosphorylation (OXPHOS). Dysfunction of these organelles is linked to a heterogeneous group of multisystemic disorders, including diabetes, cancer, ageing-related pathologies and rare mitochondrial diseases (MDs). With respect to the latter, mutations in subunit-encoding genes and assembly factors of the first OXPHOS complex (CI) induce isolated CI deficiency and Leigh syndrome (LS). This syndrome is an early-onset, often fatal, encephalopathy with a variable clinical presentation and poor prognosis due to the lack of effective intervention strategies. Mutations in the nuclear DNA (nDNA)-encoded NDUFS4 gene, encoding the NADH: Ubiquinone oxidoreductase subunit S4 (NDUFS4) of CI induce “mitochondrial complex I deficiency, nuclear type 1” (MC1DN1) and LS in pediatric patients. A variety of (tissue-specific) Ndufs4 knockout mouse models were developed to study the LS pathomechanism and intervention testing. Here, we review and discuss the role of CI and NDUFS4 mutations in human MD, and review how the analysis of Ndufs4 knockout mouse models has generated new insights into the MC1ND1/LS pathomechanism and its therapeutic targeting.