The Generalized Linear Model (GLM) is a very popular and flexible class of regression models that generalizes ordinary linear regression by allowing for example non-normal response variables. Logistic regression, which is widely used for binary classification, and Poisson regression, often used to model count data, both belong to this class. The parameters are typically estimated using maximum likelihood, but this very often leads to various problems when analyzing real data from practice. Firstly, outliers in the data may heavily influence classical methods, yielding unreliable results. Secondly, estimation and interpretability becomes very difficult or impossible when the number of variables becomes very high. Thirdly, real data often display a more complex dispersion behavior than expected under the GLM model. To solve these issues, sparse and robust estimation methods that model simultaneously the mean and the dispersion behavior in the context of GLMs will be developed. Their mathematical properties will be thoroughly investigated. The newly proposed methods should also be computationally efficient such that modern large datasets can be analyzed easily. Open-access user-friendly software will be provided.