Book excerpt: This dissertation describes the characterization of novel complex-oxide single crystals that are candidates for the discovery of new multiferroic materials and the realization of strong magnetoelectric coupling. The primary method of characterization is infrared spectroscopy in either reflection or transmission geometry, as governed by the material\U+2019\s optical response over a given frequency range. Optical properties are estimated via Kramers-Kronig relations and by fits to a Lorentz oscillator model. In certain materials, infrared results have motivated further characterization techniques: namely, magnetic susceptibility, x-ray diffraction, Raman spectroscopy, and terahertz spectroscopy. The specific materials studied are identified along with a short statement describing the major experimental findings resulting from each study. The Cu2OSeO3 system exhibited anomalous behavior of its infrared active phonons across the ferrimagnetic ordering temperature (Tc=60 K), which contributed to an abrupt change in the dielectric constant at the onset of magnetic order. The FeTe2O5Br system displayed a highly anisotropic phonon spectrum, which was corroborated by theoretical lattice dynamical calculations. In the Cu3Bi(SeO3)2O2Cl system, 16 new infrared phonons were observed below 115 K despite the lack of a structural transition, and 2 magnetic excitations were discovered below the long range magnetic ordering temperature (Tc=24 K). The Cu3(SeO3)2Cl system, which is still a work in progress, has shown drastic phonon anomalies near both 80 K and 40 K (suspected magnetic ordering temperature) suggesting the existence of a rich phase diagram.