The basic goal of cluster detection is to find regions of space where the counts are significantly higher than expected. This research has become very popular in many areas. There have been lots of tests which can be classified into tests for global clustering and tests for localized cluster. The tests for global clustering only collect evidences for clustering be present throughout the study region without determining the locations of the cluster. The weighted average likelihood ratio (WALR) test according to the weighted sum of likelihood ratios represents an important class of tests for global clustering. However, these weight functions are often defined based on the cell population size or the geographic information like area size and distances between cells. Motivated by this, this thesis develops a self-adjusted weight function to directly allocate weights onto the likelihood ratios according to their values. The spatial scan statistic test is the dominating one for localized clusters, due to its simplicity. However, this method has some potential limitations. First, it is more sensitive to the detection of cluster with larger population size but less sensitive to cluster with smaller population size, given the same change in the incidence rate of a cluster. In practice, the prior information about the locations of a potential cluster and the risk level of a disease is often unknown. So, it is necessary to develop a robust scan statistic aimed at providing an overall good performance in detecting the spatial cluster. Furthermore, the use of a scanning window of a rigid geometry has been viewed as another limitation of the spatial scan test. To deal with this limitation, the clustering methodologies based on minimum spanning tree (MST) have been widely discussed due to their simplicity and efficiency in signaling irregular clusters. However, most of the MST-based clustering methods estimate the most likely cluster based on the maximum likelihood ratio. They can only detect one cluster even if the multiple clusters are actually present over the study region. To overcome this limitation, this thesis proposes an adaptive MST (AMST) method to detect irregularly shaped clusters.