Tannaka Duality refers to the reconstruction of a compact group from its representations, while Serre's GAGA theorem relates coherent sheaves on an algebraic variety to its analytification. This talk will explore various incarnations of these two classical theorems in algebraic geometry with applications to moduli theory. This seminar is part of the activities of the Dipartimento di Eccellenza CUP B83C23001390001 and it is funded by the European Union – Next Generation EU.