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In the decade after the discovery of high-temperature superconductivity, more than one hundred non-intermetallic compounds have been found to superconduct above 23 K, which is the record transition temperature (T/sub c/) of conventional low-temperature intermetallic superconductors. These high-temperature non-intermetallic superconductors belong to three compound families: the cuprates, the bismuthates, and the fullerites. In this presentation, I shall restrict myself to the cuprates with a T/sub c/ above the liquid nitrogen boiling point of 77 K. They show a current record T/sub c/ of 134 K at ambient and 164 K at high pressure. I shall recall events that led to the discovery of superconductivity at 93 K to bring down the 77 K temperature barrier and summarize subsequent efforts to raise the T/sub c/ to its present record. Prospects for future higher T/sub c/ are discussed.