This perspective presents an overview of the development of the hierarchy of Davydov's Ans\"{a}tze and a few of its applications in many-body problems in computational chemical physics.Davydov's solitons originated in the investigations of vibrational energy transport in proteins in the 1970s.Momentum-space projection of these solitary waves turned up to be accurate variational ground-state wave functions for the extended Holstein molecular crystal model, lending unambiguous evidence to the absence of formal quantum phase transitions in the Holstein systems.The multiple Davydov Ans\"{a}tze have been proposed, with the increasing Ansatz multiplicity, as incremental improvements of their single-Ansatz parents. For a given Hamiltonian,the time-dependent variational formalism is utilized to extract accurate dynamic and spectroscopic propertiesusing Davydov's Ans\"{a}tze as its trial states.A quantity proven to disappear for large multiplicities,the Ansatz relative deviation is introduced to quantify how closely the Schr\"{o}dinger equation is obeyed.Three finite-temperature extensions to the time-dependent variation scheme are elaborated, i.e., the Monte Carlo importance sampling, the method of thermofield dynamics, and the method of displaced number states. To demonstrate the versatility of the methodology,applications of Davydov's Ans\"{a}tze are made to the generalized Holstein Hamiltonian, variants of the spin-boson model, and systems of cavity-assisted singlet fission, yielding accurate dynamic and spectroscopic properties of the many-body systems.