Inflation is an elegant paradigm for the very early Universe. It not only offers a simple solution to the flatness and horizon puzzles of the standard hot Big Bang model, but also generates quantum fluctuations that seed cosmic microwave background anisotropies and the formation of large-scale structure. In particular, both the spatial flatness of the Universe and a nearly Gaussian, scale-invariant power spectrum of the curvature perturbation predicted by inflation have been confirmed by various observations. Recently, a larger spectral index of curvature perturbation is preferred when combining with ACT DR6, and particularly when further including the H0 prior from SH0ES, and then the Starobinsky inflation model is disfavored at more than 95% confidence level. Even though modified reheating histories and non-minimal couplings have been proposed to achieve a larger value of the spectral index, the model with higher-order curvature corrections to Starobinsky inflation offers a concise and well-motivated explanation.