  The capability to probe the dispersion of elementary spin, charge, orbital,
and lattice excitations has positioned resonant inelastic x-ray scattering
(RIXS) at the forefront of photon science. In this work, we will investigate
how RIXS can contribute to a deeper understanding of the orbital properties and
of the pairing mechanism in unconventional high-temperature superconductors. In
particular, we will show how direct RIXS spectra of magnetic excitations can
reveal long-range orbital correlations in transition metal compounds, by
discriminating different kind of orbital order in magnetic and
antiferromagnetic systems. Moreover, we will show how RIXS spectra of
quasiparticle excitations in superconductors can measure the superconducting
gap magnitude, and reveal the presence of nodal points and phase differences of
the superconducting order parameter on the Fermi surface. This can reveal the
properties of the underlying pairing mechanism in unconventional
superconductors, in particular cuprates and iron pnictides, discriminating
between different superconducting order parameter symmetries, such as $s$, $d$
(singlet pairing) and $p$ wave (triplet pairing).
