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In this article we provide the updated standard-model prediction for the rare decay modes in detail, and summarise the status of standard-model prediction of $\\epsilon_K$. We find $\\text{BR}(K^+ \\to \\pi^+ \\nu \\bar \\nu) = 7.73(61) \\times 10^{-11}$ and $\\text{BR}(K_L \\to \\pi^0 \\nu \\bar \\nu) = 2.59(29) \\times 10^{-11}$. 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In this article we provide the updated standard-model prediction for the rare decay modes in detail, and summarise the status of standard-model prediction of $\\epsilon_K$. We find $\\text{BR}(K^+ \\to \\pi^+ \\nu \\bar \\nu) = 7.73(61) \\times 10^{-11}$ and $\\text{BR}(K_L \\to \\pi^0 \\nu \\bar \\nu) = 2.59(29) \\times 10^{-11}$. 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