Thioflavin-T (ThT) can bind to amyloid fibrils and is frequently used as a fluorescent marker for in vitro biomedical assays of the potency of inhibitors for amyloid-related diseases, such as Alzheimer's disease, Parkinson's disease, and amyloidosis. Upon binding to amyloid fibrils, the steady-state (time-integrated) emission intensity of ThT increases by orders of magnitude. The simplicity of this type of measurement has made ThT a common fluorescent marker in biomedical research over the last 50 years. As a result of the remarkable development in ultrafast spectroscopy measurements, researchers have made substantial progress in understanding the photophysical nature of ThT. Both ab initio quantum-mechanical calculations and experimental evidence have shown that the electronically excited-state surface potential of ThT is composed of two regimes: a locally excited (LE) state and a charge-transfer (CT) state. The electronic wave function of the excited state changes from the initial LE state to the CT state as a result of the rotation around a single C-C bond in the middle of the molecule, which connects the benzothiazole moiety to the dimethylanilino ring. This twisted-internal-CT (TICT) is responsible for the molecular rotor behavior of ThT. This Account discusses several factors that can influence the LE-TICT dynamics of the excited state. Solvent, temperature, and hydrostatic pressure play roles in this process. In the context of biomedical assays, the binding to amyloid fibrils inhibits the internal rotation of the molecular segments and as a result, the electron cannot cross into the nonradiative "dark" CT state. The LE state has high oscillator strength that enables radiative excited-state relaxation to the ground state. This process makes the ThT molecule light up in the presence of amyloid fibrils. In the literature, researchers have suggested several models to explain nonradiative processes. We discuss the advantages and disadvantages of the various nonradiative models while focusing on the model that was initially proposed by Glasbeek and co-workers for auramine-O to be the best suited for ThT. We further discuss the computational fitting of the model for the nonradiative process of ThT.