The role of astroglia in brain function has been well studied since the use of fluorescence microscopy (in vitro and in vivo two-photon imaging) began in the 1990's.
Verkhratsky and Needergaard (2018) have shown, beyond reasonable scientific doubt, that astrocytes control chemical homeostasis in the whole brain. However, the role of calcium waves in this control of homeostasis is still not consensual among the experts.
The existence of large-scale calcium waves has been proven and imaged 'in vivo' with two-photon fluorescence microscopy. Thrane et al (2012) showed that general anesthetics selectively eliminate these waves. Recently the structure of these waves has been imaged and analysed, but their function(s) is (are) still not well identified.
References:
Thrane AS, Rangroo Thrane V, Zeppenfeld D, Lou N, Xu Q, Nagelhus EA, Nedergaard M. (2012) General anesthesia selectively disrupts astrocyte calcium signaling in the awake mouse cortex. Proc Natl Acad Sci U S A.109(46):18974-9.
Verkhratsky A, Nedergaard (2018) M. Physiology of Astroglia. Physiol Rev. 98(1):239-‐389.