Abstract: Data sampled densely in space and time have become increasingly abundant as a result of advances in modern technology. However, the presence of complex dependence and current computational limitations have made many classical inferential approaches practically infeasible. In this work, we develop an ANOVA-type method for functional data that allows comparisons among groups of time series with complex spatio-temporal dependence. This work is innovative as it 1) proposes a flexible framework that accommodates a variety of tests in the ANOVA setting, 2) introduces a novel and interpretable visualization, and 3) considers spatially correlated time series. Due to its flexibility, this method is widely applicable to scientific domains where data are naturally grouped and displays complex spatio-temporal dependence. We motivate and illustrate the utility of this method in the context of several applications such as studying differences in photosynthetic activity between vegetative areas in California using satellite measurements of solar-induced chlorophyll fluorescence (SIF), the effects of experimentally simulated climate change on soil temperatures, and the social behavior of birds under stress.  A simulation study illustrates the performance of the methods in various experimental contexts. The proposed functional ANOVA methodology provides robust and interpretable tests for identifying differences between groups of curves, with broad applications to physical, environmental and life sciences.