Modern biosurveillance is the monitoring of a wide-range of pre-diagnostic and diagnostic data for the purpose of enhancing the ability of the public health infrastructure to detect, investigate, and respond to disease outbreaks. Statistical control charts have been a central tool in classic dis-ease surveillance and have also migrated into modern biosurveillance. However, the new types of data monitored, the processes underlying the time series derived from these data, and the application context all deviate from the industrial setting for which these tools were originally designed. Assumptions of normality, independence, and stationarity are typically violated in syndromic time series; target values of process parameters are time-dependent and hard to define; data labeling is ambiguous in the sense that outbreak periods are not clearly defined or known. Additional challenges arise such as multiplicity in several dimensions, performance evaluation, and practical system
usage and requirements. Our focus is mainly on the monitoring of time series for early alerting of anomalies to stimulate investigation of potential outbreaks, with a brief summary of methods to detect significant spatial and spatiotemporal case clusters. We discuss the different statistical challenges in monitoring modern biosurveillance data, describe the current state of monitoring in the field, and survey the most recent biosurveillance literature.