  The Bethe-Salpeter equation (BSE) formalism is steadily asserting itself as a
new efficient and accurate tool in the ensemble of computational methods
available to chemists in order to predict optical excitations in molecular
systems. In particular, the combination of the so-called $GW$ approximation,
giving access to reliable ionization energies and electron affinities, and the
BSE formalism, able to model UV/Vis spectra, has shown to provide accurate
singlet excitation energies with a typical error of $0.1$--$0.3$ eV. With a
similar computational cost as time-dependent density-functional theory
(TD-DFT), BSE is able to provide an accuracy on par with the most accurate
global and range-separated hybrid functionals without the unsettling choice of
the exchange-correlation functional, resolving further known issues
(\textit{e.g.}, charge-transfer excitations). In this \textit{Perspective}
article, we provide a historical overview of BSE, with a particular focus on
its condensed-matter roots. We also propose a critical review of its strengths
and weaknesses in different chemical situations.
