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We study in detail the predictions of various theoretical approaches, inparticular mode-coupling theory (MCT) and kinetically constrained models(KCMs), concerning the time, temperature, and wavevector dependence ofmulti-point correlation functions that quantify the strength of both inducedand spontaneous dynamical fluctuations. We also discuss the precise predictionsof MCT concerning the statistical ensemble and microscopic dynamics dependenceof these multi-point correlation functions. These predictions are compared tosimulations of model fragile and strong glass-forming liquids. Overall, MCTfares quite well in the fragile case, in particular explaining the observedcrucial role of the statistical ensemble and microscopic dynamics, while MCTpredictions do not seem to hold in the strong case. KCMs provide a simplifiedframework for understanding how these multi-point correlation functions mayencode dynamic correlations in glassy materials. However, our analysishighlights important unresolved questions concerning the application of KCMs tosupercooled liquids.Comment: 23 pages, 12 fig

Spontaneous and induced dynamic correlations in glass formers. II. Model calculations and comparison to numerical simulations