We introduce on-modem learning, which enables a commodity communication modem installed on commercial home appliances to perform inference and training of compact-sized DNNs (deep neural networks) to provide custom intelligent services. Given that 80-90% of commercial smart home appliances are never connected to the network, leaving computing resources of the modem idle, the proposed on-modem learning transforms a learning-incapable modem into an independent self-learning module by utilizing the unused or under-utilized modem resources. To this end, we propose an on-modem DNN inference framework consisting of Data Payload Parser and On-Modem DNN engine. We also propose an on-modem DNN training framework, which enables resource-efficient training of DNNs on the modem via Greedy and Diverse Gradient Accumulation (GDGA), Dynamic Programming-based Back-Propagation (DPBP), and On-Modem Reinforcement Learning (OMRL). To the best of our knowledge, the proposed on-modem learning is the first to execute DNN inference and training on the modem of commercial home appliances. To validate the efficacy of on-modem learning, we implement two on-modem learning applications on the real LG Electronics washing machine, i.e., (1) remaining wash time prediction and (2) UE (unbalance error) forecasting. Our experiment shows that on-modem learning successfully conducts DNN inference and training on the modem of commercial home appliances and provides custom intelligent services to end users.