  The search for new wide band gap materials is intensifying to satisfy the
need for more advanced and energy efficient power electronic devices.
Ga$_2$O$_3$ has emerged as an alternative to SiC and GaN, sparking a renewed
interest in its fundamental properties beyond the main $\beta$-phase. Here,
three polymorphs of Ga$_2$O$_3$, $\alpha$, $\beta$ and $\varepsilon$, are
investigated using X-ray diffraction, X-ray photoelectron and absorption
spectroscopy, and ab initio theoretical approaches to gain insights into their
structure - electronic structure relationships. Valence and conduction
electronic structure as well as semi-core and core states are probed, providing
a complete picture of the influence of local coordination environments on the
electronic structure. State-of-the-art electronic structure theory, including
all-electron density functional theory and many-body perturbation theory,
provide detailed understanding of the spectroscopic results. The calculated
spectra provide very accurate descriptions of all experimental spectra and
additionally illuminate the origin of observed spectral features. This work
provides a strong basis for the exploration of the Ga$_2$O$_3$ polymorphs as
materials at the heart of future electronic device generations.
