  Interesting phenomena and problems arising from the coupling of large-scale
electromagnetic fields and spacetime curvature, are introduced and studied
within this thesis. From electromagnetic wave propagation in curved spacetime
to envisaging a gravito-electromagnetic equivalence on large scales; from
magnetic fields' cosmic evolution, and magnetised gravitational collapse in
astrophysical environments, to the interaction between electromagnetic and
gravitational radiation; the present research work explores some unique
characteristics and properties of the gravito-electromagnetic coexistence. Its
theoretical framework is generally provided by classical (Maxwellian)
electrodynamics in the (4-dimensional) Riemannian spacetime of General
Relativity. Chapter 1, dealing with the perspective of a
gravito-electromagnetic equivalence in a metric affine geometry (involving
torsion and non-metricity), forms an exception to the aforementioned general
framework. Regarding its structure, the manuscript consists of four chapters
divided in two parts. The first two chapters (forming Part I) are concerned
with the Maxwell field in curved, Riemannian (Chapter 2) and (generalised)
metric affine (Chapter 2), spacetime framework. Aspects of the Weyl-Maxwell
coupling (where the Weyl field refers to long-range curvature) are also
included in Chapter 2. The last two chapters (forming Part II) treat
magnetohydrodynamics in the general relativistic framework.
