Logical models for cellular signaling networks are recently attracting wide interest: Their ability to integrate qualitative information at different biological levels, from receptor-ligand interactions to gene-regulatory networks, is becoming essential for understanding complex signaling behavior. We present an overview of Boolean modeling paradigms and discuss in detail an approach based on causal logical interactions that yields descriptive and predictive signaling network models. Our approach offers a mathematically well-defined concept, improving the efficiency of analytical tools to meet the demand of large-scale data sets, and can be extended into various directions to include timing information as well as multiple discrete values for components.