Multi-modal spatio-temporal analysis is aimed at discovering valuable knowledge about the spatio-temporal distributions, associations and revolutions underlying the multi-modal geographic big data. It is a core task of the pan-spatial information system, and is expected to facilitate the study of relationship between human and space. With emerging opportunities and challenges in an era of geographic big data, we systematically summarized four main methods for spatial-temporal analysis based on previous study, including spatio-temporal cluster analysis, spatio-temporal outlier detection, spatio-temporal association mining and spatio-temporal prediction. We discussed the challenges when applying the four methods in multi-scale modeling, multi-view fusion, multi-characteristic cognition, and multi-characteristic expression for spatial-temporal analysis. First, two types of scales (including data scale and analysis scale) are of great importance in the spatio-temporal clustering task. Given the data scale, the best analysis scale for detecting spatio-temporal clusters can be determined using a permutation test method by evaluating the significance of clusters. Second, in the spatio-temporal outlier detection method, the cross-outliers in the context of two types of points are known as the abnormal associations between different types of points and the validity of cross-outliers is assessed through significance tests under the null hypothesis of complete spatial randomness. Third, in the spatio-temporal association mining method, the multi-modal distribution characteristics of each feature quantitatively described in the observed dataset are employed to construct the null hypothesis that the spatio-temporal distributions of different features are independent of each other, and then the evaluation of spatio-temporal associations is modeled as a significance test problem under the null hypothesis of independence. Finally, in the spatio-temporal prediction model, the effects of multiple characteristics of spatio-temporal data (e.g., spatio-temporal auto-correlation and heterogeneity) on the prediction results are fully considered using a space-time support vector regression model. These methods can reveal the geographic knowledge in a more comprehensive, objective, and accurate way, and play a key role in supporting the smart city applications, such as meteorological and environmental monitoring, public safety management, and urban facility planning. For example, the spatio-temporal clustering method can be used to identify the meteorological division, the spatio-temporal outliers can contribute to the detection of the abnormal distribution of urban facilities, the spatio-temporal association mining method can help discover and understand the relationship among different types of crimes, and the spatio-temporal prediction method can be employed to predict the concentration of air pollutants.