Two-photon absorption (TPA) is a nonlinear optical process in which an atom or molecule is excited by the simultaneous absorption of two photons. This phenomenon was initially proposed by Göppert-Mayer in 1931, and experimentally confirmed only 30 years later by Kaiser and collaborators. The TPA process can be quantified by the probability of absorption of two photons, which is usually reported as a crosssection (𝜎 TPA ). In contemporary applications, materials or dyes exhibiting substantial 𝜎 TPA are extensively used in various technological fields, including optical data storage, 3D microfabrication, optical power limit, bioimaging, and photodynamic therapy. For example, bioimaging applications require the product of two-photon absorption cross-section and fluorescence quantum yield larger than 50 GM (1 GM = cm •s•photon ). In the case of organic dyes 𝜎 TPA values can reach several thousands of GM. During the past five decades, computational quantum chemistry has evolved into an indispensable tool for interpreting experimental TPA measurements. Indeed theoretical calculations provide valuable insights into structure/properties relationships and furthermore, they can be routinely employed to design new molecules with significant 𝜎 TPA , obviating the need for generally expensive and complex experiments. The 𝜎 TPA for the absorption of two photons having the same frequency can be expressed as: