Developments in observational astrophysics are producing higher-quality data at increasingly immense volumes. As a result, the requirements for reference data on the properties of atoms in astrophysics are no longer met. This thesis aims to address this problem, primarily through high-resolution Fourier transform spectroscopy of laboratory atomic plasmas of elements of urgent astrophysical needs, which include the rare-earth and iron-group elements that are of particular interest in nucleosynthesis and stellar structure investigations, owing to their complex spectra and intriguing cosmic relative abundances. The spectrum and atomic structure of the second ionisation stage of the rare-earth element neodymium (Nd III, 60 protons) were very poorly known experimentally. Spectra of Nd were recorded in the region 11500-54000 /cm (870-185 nm) using resolving powers up to 10^6 and measured wavenumbers were accurate to a few parts in 10^8. Analysis of the Nd spectra was supplemented by grating spectroscopy and semi-empirical atomic structure calculations. Overall, 258 energy levels and 957 transitions of Nd III have been identified, where 219 energy levels were identified for the first time. The high-resolutions of modern astrophysical spectra can also observe the hyperfine structure of atomic energy levels, which cause distortion and broadening of spectral lines and must be considered in stellar spectral line modelling. For the first ionisation stage of the iron-group element cobalt (Co II, 27 protons), hyperfine structure constants of only 28 of the ~500 experimentally known energy levels were previously investigated. The analysis of Co Fourier transform spectra led to the determination of the magnetic dipole interaction constants for 298 energy levels of Co II, 264 of which were determined for the first time. The order of magnitude increase in the available atomic reference data for Nd III energy levels and Co II hyperfine structure will enable wider and more reliable applications of these elements in astrophysical investigations.