This thesis presents an experimental and theoretical study of the alkaline earth atoms, strontium and barium, isolated in rare gas matrices (argon, krypton and xenon) at cryogenic temperatures. These solid-state M/RG (M = Sr and Ba; RG = Ar, Kr and Xe) samples are extensively characterised using time-integrated (steady-state) and time-resolved spectroscopic techniques. The primary goal of this work is to develop the spectroscopy of matrix-isolated Group II metals and augment the ongoing research of the Maynooth Group, which focuses on S metal atom – rare gas systems. Moreover, the literature on the spectroscopy of matrix-isolated Sr or Ba is quite sparse and the limited number of reports that do exist contain inaccuracies, which are in need of clarification and amendment. M/RG samples deposited at 10 K, under conditions of low metal loading, consist of well-isolated metals atoms. Conversely, matrices formed at elevated temperature contain a higher yield of metal clusters. Absorption spectra recorded of M/RG solids condensed onto a ‘warm’ sample window reveal the presence of additional non-atomic features – these are attributed to metal dimers based on the low metal fluxes employed during deposition. Further characterisation of the Group II diatomics was accomplished using steady-state and time-resolved luminescence spectroscopy. The luminescence produced with excitation of the metal dimer absorption bands reveals very different behaviour for Sr2/RG and Ba2/RG. Resonance fluorescence with a lifetime of 15 ns is observed for the lowest energy transition of Sr2. In contrast, the lowest energy transition of Ba2 is completely quenched – this behaviour is consistent with the absence of vibrational structure on the near-IR absorption band of Ba2, indicating that a lifetime broadening effect exists on this molecular transition. Moreover, the excitation/emission features identified in the visible spectral region (580 – 680 nm) for matrix-isolated Ba2, likely originate from molecular states of the dimer, which dissociate to atomic asymptotes existing above the (6s6p) 1P1 level of the atom. The (nsnp) 1P ← (ns2) 1S resonance transitions, which occur in the visible spectral region, are used to compare the isolation conditions of these two metal atom systems. Complex and structured absorption bands were recorded for both Sr and Ba in all three hosts, even after extensive sample annealing. Thus, these alkaline earth atoms occupy a myriad of thermally stable sites in solid Ar, Kr and Xe matrices. As a result, each M/RG solid exhibits numerous (nsnp) 1P emission bands and two dimensional – excitation and emission (2D-EE) spectra are required to fully unravel the luminescence. The excitation spectra extracted from the 2D-EE scans allow the complex absorption bands to be resolved into site-specific features. Both metal atom systems display a variety of excitation patterns, ranging from the classic Jahn-Teller threefold split, to asymmetric threefold (2+1) patterns and broad, unstructured bands. It is therefore concluded that the isolation of Sr and Ba atoms in rare gas solids occurs in cubo-octahedral, crystalline (fcc) sites on one hand and in non-crystalline sites on the other. To assist the interpretation of the site occupancy, novel ground state potential energy curves are computed for the 1:1 M·RG complexes (M=Ca, Sr, Ba and RG = Ar, Kr, Xe), using the empirical Tang-Toennies (TT) and ab initio CCSD(T) methods. The spectroscopic constants obtained from both approaches were in agreement. Long bond lengths (> 5 Å) and shallow bound regions (<142 cm-1) were revealed for the nine M·RG diatomics. Although the TT model is computationally inexpensive and accurately describes the long range, attractive portion of the potential energy curves, the poor performance of this function at describing the inner repulsive walls precludes the use of this method in analysing the M/RG matrix systems. Thus, the site occupancy was interpreted using only the ab initio results. A comparison of the M·RG (coupled-cluster) and RG2 potential energy curves allowed for comments to be made regarding the occupancy of the alkaline earth atoms within cubic sites of the fcc rare gas lattices. Combining the theoretical analysis with the site-specific (nsnp) 1P1 excitation spectra recorded in annealed matrices yielded tentative site assignments. In summary, the ‘blue’ sites of isolation are tentatively assigned to tetra-vacancies (TVs) and the ‘green’ sites to hexa-vacancies (HVs). The ‘violet’ and ‘R1’ trapping sites produce an asymmetric threefold (2+1) pattern in absorption/excitation, inferring a non-isotropic environment removes the degeneracy of the excited (nsnp) 1P state. Accordingly, these sites are proposed as cylindrically shaped voids (CV). The atomic (nsnp) 1P1 luminescence recorded in RG matrices reveals contrasting behaviour for Sr and Ba atoms. Only resonance (6s6p) 1P1 → (6s2) 1S0 emission was observed for Ba/RG solids – scans made out to 900 nm (the limit of our detection system) do not reveal any lower energy features. Conversely, the luminescence of Sr/RG solids is richer as emissions arising from the (5s5p) 1P1, (5s4d) 1D2, (5s4d) 3D1 and (5s5p) 3P1 excited states of Sr are identified. In addition, the 1D2 state of atomic Sr can be readily accessed in absorption, therefore allowing investigation of the (5s4d) 1D2 luminescence. For both metal atom systems, state assignments were made based on the observed spectral (location and bandwidth) and temporal characteristics. For example, the resonance (nsnp) 1P1 emission bands exhibit nanosecond radiative lifetimes (< 10 ns). In contrast, the 3D1 and 3P1 emission features of Sr exhibit microsecond radiative lifetimes (> 1 μs). The results presented in this thesis demonstrate that the site of isolation critically governs the excited state guest/host interactions and the photophysical properties observed. However, temperature studies also reveal the existence of a host dependence. As a result, it is proposed that intersystem crossings occur in both metal atom systems and the efficiency of these processes are greatest in solid Xe due to the external heavy atom effect. For Ba, it is suggested that a 1P1 → 3P2 relaxation pathway competes with the resonance fluorescence and is most active in Xe at elevated temperatures. Similarly, it is proposed that non-radiative 1P1, 1D2 → 3DJ transitions strongly influence the luminescence of atomic Sr in RG solids, even at low temperature (10 K).