This review discusses non-Gaussianities in primordial black hole (PBH) formation and induced gravitational waves (GWs). The most promising mechanism for generating PBHs is through an enhanced power spectrum of the primordial curvature perturbation, which is often accompanied by non-Gaussianity that significantly affects PBH abundance. Non-Gaussianity can arise in single-field inflation and the curvaton scenario. The PBH mass function and induced GWs are calculated considering these non-Gaussianities. While non-Gaussianity has a mild impact on the spectral shape of induced GWs, it significantly affects PBH abundance. The induced GWs depend on the variance of the curvature perturbation's PDF, while PBH abundance depends on the high-σ tail of the PDF. A small deviation from Gaussianity can lead to large changes in PBH abundance but only minor changes in GW amplitude. Non-Gaussianity is often described by the perturbative series, which is also used for PBH formation and induced GWs. In many models, the non-linear parameter $ f_{NL} $ reaches $ O(1) $, making higher-order terms important. The $ \delta N $ formalism allows for the calculation of the curvature perturbation in single-field inflation and the curvaton scenario. The Press-Schechter-type formalism and the theory of peaks are used to calculate PBH abundance. Non-Gaussianity can lead to clustered PBHs, enhancing merger rates and affecting GW detection. The power spectrum of curvature perturbations on small scales can be enhanced, but loop corrections on CMB scales may jeopardize this. Smooth transitions from ultra-slow-roll to slow-roll inflation can lead to Gaussian or non-Gaussian curvature perturbations. The curvaton scenario generates curvature perturbations from the decay of the curvaton field. Non-Gaussianity in PBH formation and induced GWs is important for theoretical and observational issues in cosmology.This review discusses non-Gaussianities in primordial black hole (PBH) formation and induced gravitational waves (GWs). The most promising mechanism for generating PBHs is through an enhanced power spectrum of the primordial curvature perturbation, which is often accompanied by non-Gaussianity that significantly affects PBH abundance. Non-Gaussianity can arise in single-field inflation and the curvaton scenario. The PBH mass function and induced GWs are calculated considering these non-Gaussianities. While non-Gaussianity has a mild impact on the spectral shape of induced GWs, it significantly affects PBH abundance. The induced GWs depend on the variance of the curvature perturbation's PDF, while PBH abundance depends on the high-σ tail of the PDF. A small deviation from Gaussianity can lead to large changes in PBH abundance but only minor changes in GW amplitude. Non-Gaussianity is often described by the perturbative series, which is also used for PBH formation and induced GWs. In many models, the non-linear parameter $ f_{NL} $ reaches $ O(1) $, making higher-order terms important. The $ \delta N $ formalism allows for the calculation of the curvature perturbation in single-field inflation and the curvaton scenario. The Press-Schechter-type formalism and the theory of peaks are used to calculate PBH abundance. Non-Gaussianity can lead to clustered PBHs, enhancing merger rates and affecting GW detection. The power spectrum of curvature perturbations on small scales can be enhanced, but loop corrections on CMB scales may jeopardize this. Smooth transitions from ultra-slow-roll to slow-roll inflation can lead to Gaussian or non-Gaussian curvature perturbations. The curvaton scenario generates curvature perturbations from the decay of the curvaton field. Non-Gaussianity in PBH formation and induced GWs is important for theoretical and observational issues in cosmology.