Bardeen–Cooper–Schrieffer (BCS) theory, where electrons form Cooper pairs through phonon interactions. However, high-temperature superconductors, such as cuprates and iron-based compounds, cannot be fully explained by this model. Evidence suggests that strong electron correlations and magnetic fluctuations play a key role in their pairing mechanism. Moreover, the pseudogap phase observed in cuprates indicates a possible competing electronic order. Advanced techniques like angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM) have provided valuable insights, yet a unified microscopic theory is still missing. Understanding these mechanisms remains one of the central challenges in modern physics.