BACKGROUND: Data visualisation has become an integral part of statistical modelling. METHODS: We present visualisation methods for preliminary exploration of time-series data, and graphical diagnostic methods for modelling relationships between time-series data in medicine. We use exploratory graphical methods to better understand the relationship between a time-series reponse and a number of potential covariates. Graphical methods are also used to examine any remaining information in the residuals from these models. RESULTS: We applied exploratory graphical methods to a time-series data set consisting of daily counts of hospital admissions for asthma, and pollution and climatic variables. We provide an overview of the most recent and widely applicable data-visualisation methods for portraying and analysing epidemiological time series. DISCUSSION: Exploratory graphical analysis allows insight into the underlying structure of observations in a data set, and graphical methods for diagnostic purposes after model-fitting provide insight into the fitted model and its inadequacies.