The paper introduces distributed lag non-linear models (DLNMs), a flexible statistical framework for modeling the relationship between environmental exposures and health outcomes, accounting for both non-linear effects and delayed responses. DLNMs use a 'cross-basis' approach, combining two-dimensional functions to simultaneously describe the exposure-response relationship and the lag dimension. This method extends traditional distributed lag models (DLMs) by allowing for non-linear and time-varying effects, providing a unified framework for various modeling approaches. The DLNM is implemented in the R package dlnm, and is illustrated using data from the National Morbidity, Mortality, and Air Pollution Study (NMMAPS) to examine the relationship between temperature and mortality in New York (1987–2000). The results show a strong immediate effect of heat, with delayed effects for extreme temperatures, and a more prolonged effect for cold temperatures. DLNMs offer a more flexible and accurate representation of complex exposure-response relationships compared to simpler models. The paper discusses the application of DLNMs in environmental and health studies, emphasizing their ability to capture both non-linear and time-delayed effects, and highlights the importance of model selection and sensitivity analysis in ensuring robust results. The methodology is implemented in R, and the package is publicly available for further use.The paper introduces distributed lag non-linear models (DLNMs), a flexible statistical framework for modeling the relationship between environmental exposures and health outcomes, accounting for both non-linear effects and delayed responses. DLNMs use a 'cross-basis' approach, combining two-dimensional functions to simultaneously describe the exposure-response relationship and the lag dimension. This method extends traditional distributed lag models (DLMs) by allowing for non-linear and time-varying effects, providing a unified framework for various modeling approaches. The DLNM is implemented in the R package dlnm, and is illustrated using data from the National Morbidity, Mortality, and Air Pollution Study (NMMAPS) to examine the relationship between temperature and mortality in New York (1987–2000). The results show a strong immediate effect of heat, with delayed effects for extreme temperatures, and a more prolonged effect for cold temperatures. DLNMs offer a more flexible and accurate representation of complex exposure-response relationships compared to simpler models. The paper discusses the application of DLNMs in environmental and health studies, emphasizing their ability to capture both non-linear and time-delayed effects, and highlights the importance of model selection and sensitivity analysis in ensuring robust results. The methodology is implemented in R, and the package is publicly available for further use.