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In this survey article, we discuss the algebraic structure of q-analogues ofmultiple zeta values, which are closely related to derivatives of Eisensteinseries. Moreover, we introduce the formal double Eisenstein space, whichgeneralizes the formal double zeta space of Gangl, Kaneko, and Zagier. Usingthe algebraic structure of q-analogues of multiple zeta values, we will presenta realization of this space. As an application, we will obtain purelycombinatorial proofs of identities among (quasi-)modular forms.

q-analogues of multiple zeta values and the formal double Eisenstein space