  The aim of this brief review is twofold. First, we give an overview of the
unprecedented experimental efforts to measure the gravitational acceleration of
antimatter; with antihydrogen in three competing experiments at CERN (AEGIS,
ALPHA and GBAR, and with muonium and positronium in other laboratories in the
world. Second, we present the 21st Century's attempts to develop a new model of
the Universe with the assumed gravitational repulsion between matter and
antimatter; so far, three radically different and incompatible theoretical
paradigms have been proposed. Two of these 3 models, Dirac-Milne Cosmology
(that incorporates CPT violation) and the Lattice Universe (based on CPT
symmetry) assume a symmetric Universe composed of equal amounts of matter and
antimatter, with antimatter somehow "hidden" in cosmic voids; this hypothesis
produced encouraging preliminary results. The hearth of the third model is the
hypothesis that quantum vacuum fluctuations are virtual gravitational dipoles;
for the first time, this hypothesis makes possible and inevitable to include
the quantum vacuum as a source of gravity. Standard Model matter is considered
as the only content of the Universe, while phenomena usually attributed to dark
matter and dark energy are explained as the local and global effects of the
gravitational polarization of the quantum vacuum by the immersed baryonic
matter. An additional feature is that we might live in a cyclic Universe
alternatively dominated by matter and antimatter. In about three years, we will
know if there is gravitational repulsion between matter and antimatter; a
discovery that can forever change our understanding of the Universe.
