To mitigate drought losses, identification, categorization, and prediction of droughts are essential. The objectives of this dissertation research are (1) to improve drought identification in cold climate regions by developing a new hydroclimatic aggregate drought index (HADI) and a snow-based hydroclimatic aggregate drought index (SHADI), (2) to customize drought categorization by considering both spatial and temporal distributions of droughts, and (3) to improve drought prediction by modifying the traditional support vector regression (SVR). R-mode principal component analyses (PCA) are conducted for rainfall, snowmelt, surface runoff, and soil water storage to derive the HADI. Instead of rainfall and snowmelt in the HADI, precipitation and snowpack are used to estimate the SHADI for adding the capability of snow drought identification. Drought frequencies and classes form a bivariate distribution function by applying a joint probability distribution function. A conditional expectation is further used to estimate the probability of occurrence of droughts. To derive variable threshold levels for drought categorization, hierarchical K-means clustering is used. For drought prediction, a change point detection method is employed to split the non-stationary time series into multiple stationary time series. SVR is further performed on each stationary time series to predict drought. The new drought methods were applied to the Red River of the North Basin (RRB). The 1979-2010 and 2011-2016 data obtained from the North American land data assimilation system were used for training and testing, respectively. Precipitation, temperature, and evapotranspiration were selected as the predictors, and the target variables consisted of multivariate HADI and SHADI, bivariate standardized drought indices, and univariate standardized drought indices. The results showed that the new HADI and SHADI, together with the customized drought categorization, were able to provide more accurate drought identification and characterization, especially for cold climate regions. The comparison of the results of the traditional and modified SVR models in the RRB demonstrated better performance of the modified SVR, particularly when drought indices with higher sensitivity to temperature were used. The methodologies developed in this dissertation research can be used for improving drought identification, categorization, and prediction, as well as further mitigating the potential adverse impacts of droughts.