Theories of chemical structure were first developed by August Kekulé, Archibald Scott Couper, and Aleksandr Butlerov, among others, from about 1858.  These theories were first to state that chemical compounds are not a random cluster of atoms and functional groups, but rather had a definite order defined by the valency of the atoms composing the molecule, giving the molecules a three dimensional structure that could be determined or solved.
Concerning chemical structure, one has to distinguish between pure connectivity of the atoms within a molecule (chemical constitution), a description of a three-dimensional arrangement (molecular configuration, includes e.g. information on chirality) and the precise determination of bond lengths, angles and torsion angles, i.e. a full representation of the (relative) atomic coordinates.
In determining structures of chemical compounds, one generally aims to obtain, first and minimally, the pattern and degree of bonding between all atoms in the molecule; when possible, one seeks the three dimensional spatial coordinates of the atoms in the molecule (or other solid).