In a multiple regression with high-dimensional predictors, it is usually desired to select important variables or groups of variables. Traditional penalization methods such as lasso and bridge, and their group versions, such as group lasso and group bridge, have been well established for variable selection and group selection. However, in many scientific areas, prior knowledge is available about the importance of predictors or grouped predictors, leading to the necessity of methodological development to incorporate such valuable information. For prior-informative variables and groups of variables, we develop new penalization methods called “prior lasso” and “group ridge”, respectively, to incorporate such prior information into high-dimensional generalized linear models. When the prior information is relatively accurate, both methods are shown to possess theoretical and empirical advantages over their traditional counterparts through asymptotic theories and simulation studies. When the prior information is less reliable, both methods are shown to be robust to the misspecification. We also illustrate the applicability and efficacy of both methods using real data sets from genome-wide association studies.