This paper mainly reviews the work on the physical system design of the liquid?nitrogen?cooled ⁴⁰Ca⁺ optical clock, the evaluation of its uncertainty and the optimization of the stability for the ⁴⁰Ca⁺ optical clocks in the Innovation Academy for Precision Measurement Science and Technology of the Chinese Academy of Sciences. The liquid?nitrogen?cooled system creates a liquid?nitrogen temperature environment (～ 80 K) for the ⁴⁰Ca⁺, which greatly reduces the blackbody radiation (BBR) frequency shift of the ⁴⁰Ca⁺ optical clock, and improve its systematic uncertainty to 3.0?×?10^-18, becoming the fifth type of atomic/ion optical clocks with uncertainty reaching to the 10^-18 level. In order to optimize the stability of the ⁴⁰Ca⁺ optical clock, the clock laser frequency was referenced to the Ramsey fringe, and the reference fringe determination algorithm and the automatic peak?finding algorithm were introduced, making the ⁴⁰Ca⁺ optical clocks run stably for a long time and reach a stability of 6.3?×?10^-18 with an averaging time of 524 000 s.