Fast changes in human demographics worldwide, coupled with increased mobility, and modified land uses make the threat of emerging infectious diseases increasingly important. Currently there is worldwide alert for H5N1 avian influenza becoming as transmissible in humans as seasonal influenza, causing a pandemic of unprecedented proportions. Here we show how epidemiological surveillance data for emerging infectious diseases can be interpreted in real time to assess changes in transmissibility with quantified uncertainty, and to perform running time predictions of new cases and logistical allocations. We develop an extension of standard epidemiological models, appropriate for emerging infectious diseases, that describes the probabilistic progression of case numbers due to the concurrent effects of (incipient) human transmission and multiple introductions from a reservoir. The model is cast in terms of surveillance observables and immediately suggests a simple graphical estimation procedure for the basic reproductive number R0 of standard epidemics. For emerging infectious diseases, which typically show large case number fluctuations over time, we develop a Bayesian procedure that results in estimation of the full probability distribution for R0. This knowledge is used in turn to formulate statistical tests on future case numbers for changes in the epidemiological status of emerging diseases. We use information released by the World Health Organization to place bounds on the R0 of H5N1 influenza in humans, and establish a statistical basis for monitoring its epidemiological evolution. This approach enables quantitative guidance for designing new primary prevention strategies to contain emerging infectious diseases before they become epidemic.