This paper introduces a path-following algorithm for $L_1$-regularized generalized linear models (GLMs). The $L_1$-regularization procedure is particularly useful for variable selection, as it penalizes the $L_1$-norm of the coefficients, leading to a less greedy selection process compared to forward selection–backward deletion. The algorithm efficiently computes solutions along the entire regularization path using the predictor–corrector method of convex optimization. The step length of the regularization parameter is crucial for controlling the overall accuracy of the paths, and the authors suggest intuitive and flexible strategies for selecting appropriate values. The implementation is demonstrated with several simulated and real data sets, including a microarray dataset with over 7000 genes. The paper also extends the method to the Cox proportional hazards model and discusses its application in gene selection. The algorithm is implemented in the R package glmpath.This paper introduces a path-following algorithm for $L_1$-regularized generalized linear models (GLMs). The $L_1$-regularization procedure is particularly useful for variable selection, as it penalizes the $L_1$-norm of the coefficients, leading to a less greedy selection process compared to forward selection–backward deletion. The algorithm efficiently computes solutions along the entire regularization path using the predictor–corrector method of convex optimization. The step length of the regularization parameter is crucial for controlling the overall accuracy of the paths, and the authors suggest intuitive and flexible strategies for selecting appropriate values. The implementation is demonstrated with several simulated and real data sets, including a microarray dataset with over 7000 genes. The paper also extends the method to the Cox proportional hazards model and discusses its application in gene selection. The algorithm is implemented in the R package glmpath.