Drug resistance is a major cause of tumor mortality. Signaling networks became useful tools for driving pharmacological interventions against cancer drug resistance. Signaling datasets now cover the entire human cell. Recently, network adaptation became understood as a learning process. We review rapidly increasing evidence showing that the development of cancer drug resistance can be described as learning of signaling networks. During drug adaptation, the network forgets drug-affected pathways by desensitization and relearns by strengthening alternative pathways. Thus, resistant cancer cells develop a drug resistance memory. We show that all key players of cellular learning (i.e., IDPs, protein translocation, microRNAs/lncRNAs, scaffolding proteins and epigenetic/chromatin memory) have important roles in the development of cancer drug resistance. Moreover, all of them are central components of the epithelial-mesenchymal transition leading to metastases and resistance. Phenotypic plasticity was recently listed as a hallmark of cancer. We review how network plasticity induces rare, pre-existent drug-resistant cells in the absence of drug treatment. Key network methods assessing the development of drug resistance and network pharmacological interventions against drug resistance are summarized. Finally, we highlight the class of cellular memory drugs affecting cellular learning and forgetting, and we summarize current challenges to prevent or break drug resistance using network models.