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The suitability of the time-dependent density-functional theory (TDDFT) approach for the theoretical study of the optical properties of biomolecules is demonstrated by several examples. We critically discuss the limitations of available TDDFT implementations to address some of the present open questions in the description of the excited-state dynamics of biological complexes. The key objective of the present work is to address the performance of TDDFT in the linear response regime of the bio-molecular systems to the visible or near UV radiation – measured by, e.g. optical absorption or optical dichroism spectra. Although these spectra are essentially determined by the electronic degrees of freedom of small, optically active regions within the usually large biological systems, they can also be strongly influenced by environment effects (solvent, hosting protein, temperature, etc.). Moreover, many key biological processes consist of photo-induced dynamics (photoisomerisation, etc.), and their description requires a coupled treatment of electronic and nuclear degrees of freedom. We illustrate these aspects with a selection of paradigmatic biomolecular systems: chromophores in fluorescent proteins, porphyrins, DNA basis, the azobenzene dye, etc.