Public health surveillance provides information to identify public health problems and respond appropriately when they occur. This information is crucial to prevent and control a variety of health conditions such as infectious diseases, chronic diseases, injuries, or health-related behaviors. Quality surveillance is needed to understand the true health status of the population and to guide the use of limited public health resources. Under inadequate surveillance systems, leaders are grossly misinformed and may lose opportunities for the application of early prevention and control measures. In these situations, it is possible the resurgence of previously eradicated diseases or the uncontrolled global spread of diseases as in the case of HIV/AIDS. Surveillance involves four main integrated activities: the collection of health data, the analyses and interpretation of these data, and the timely dissemination of the results to those responsible to respond to a population's health needs. Surveillance systems capture spatial, temporal and person characteristics on health outcomes. Incidence and mortality rates quantify the size of the health problem in a given population and provide the basis for initiating disease control measures and evaluating their effectiveness. Temporal trends and demographic and ethnic group comparisons can provide important clues as to disease etiology. The increased availability of geographically georeferenced health and population data, and the development of geographic information systems (GIS) and software for geocoding addresses, have facilitated the ascent of the investigations of spatial and spatio-temporal variations of disease. There is a wide range of spatial and spatio-temporal methods that can be applied as a surveillance tool including disease mapping, clustering, and geographic correlation studies. Many of these methods may be used for detecting unusual geographic or temporal variation in disease risk, highlighting areas at apparently high risk, early detection of epidemics, detecting significant disease clusters in space and time, assessing the risk in relation to a putative source, and identifying factors associated with the spatial distribution of disease. Unfortunately, naive use of the statistical methods can be highly misleading. Therefore, a thorough understanding of potential problems such as changes in case definitions and completeness issues are critical to the analysis of the data and interpretation of the findings. Over the past few decades, surveillance has undergone considerable development. Certain activities have contributed to the advance of public health surveillance. These include technological innovations such as real-time on-line monitoring and advances in GIS, the development of new statistical methods and computational tools to apply them, and more effective use of electronic media and other tools of communications that facilitate dissemination of surveillance information for public health practice. Also, public health surveillance has changed in response to new public health concerns, such as bioterrorist events and relatively new diseases and epidemics, such as severe acute respiratory syndrome (SARS). As public health needs change and new tools and increased computational capacity of computers become available, statistical methods for disease surveillance must continue to evolve to improve the quality of the analyses, and the interpretation and display of the results in the most useful form and appropriate time-frame to meet the interests of policymakers and stakeholders. The aim of this thesis is to propose new techniques for helping public health surveillance practice. In particular, we focus in spatial and spatio-temporal methods that can help deal with missing data (Chapter 4), model the correlated heterogeneity in disease mapping (Chapter 5), detect spatial and spatio-temporal clusters (Chapter 6), and elucidate spatial variations in temporal trends (Chapter 7).