This chapter discusses the high-level computational investigations that have identified the low-lying weak bands, in the red-side region of the absorption spectrum of several diradicaloids, as due to the double-exciton state. It also discusses cost-effective density functional theory-based computational approaches that can capture, with suitable accuracy, the excitation energies of these low-lying electronic states. Diradicaloids have been proposed as candidates for a variety of applications in materials science, such as ambipolar organic field effect transistors, singlet fission in organic photovoltaics, near infrared absorption, large two-photon absorption, and thermally convertible spin states. Double excitations can be recovered from TDDFT calculations also with the SF scheme. SF-TDDFT treats ground- and excited-state electron correlation on the same footing, while also incorporating some doubly excited configurations that are important for biradicals. A reliable prediction of the excited states and excitation energies of conjugated diradicaloids is challenging because of correlation effects and multi-reference methods that ensure the appropriate level of electron correlation.