Spatial surveillance is a special case of multivariate surveillance. Thus, in this review of spatial outbreak methods, the relation to general multivariate surveillance approaches is discussed. Different outbreak models are needed for different public health applications. We will discuss methods for the detection of: 1) Spatial clusters of increased incidence, 2) Increased incidence at only one (unknown) location, 3) Simultaneous increase at all locations, 4) Outbreaks with a time lag between the onsets in different regions. Spatial outbreaks are characterized by the relation between the times of the onsets of the outbreaks at different locations. The sufficient reduction plays an important role in finding a likelihood ratio method. The change at the outbreak may be a step change from the non-epidemic period to an increased incidence level. However, errors in the estimation of the baseline have great influence and nonparametric methods are of interest. For the seasonal influenza in Sweden the outbreak was characterized by a monotonic increase following the constant non-epidemic level. A semiparametric generalized likelihood ratio surveillance method was used. Appropriate evaluation metrics are important since they should agree with the aim of the application. Evaluation in spatial and other multivariate surveillance requires special concern.