This doctoral thesis presents new experimental findings on high-spin states and their theoretical implications to the region of medium-mass (50<Z, N<82) transitional nuclei. Detailed experimental data on high-spin structures in A≈130 nuclei are exploited to benchmark the reliability of shell-model calculations in the area northwest of doubly-magic nucleus 132Sn. The findings are based upon the synergies between different cutting-edge nuclear spectroscopy experiments, relying on multinucleon-transfer reactions using the high-efficient Advanced GAmma Tracking Array (AGATA) coupled in series with the tracking magnetic spectrometer PRISMA located at the Laboratori Nazionali di Legnaro, Italy, and precise fusion-evaporation reactions at the HORUS spectrometer at the FN tandem accelerator of the University of Cologne, Germany. Xe and Ba isotopes near the 50<Z, N<82 shell closures can not be efficiently populate during fusion-evaporation experiments with reasonable production yields. Weak reaction channels which evaporate charged particles like protons require careful preconditions for a detailed spectroscopy. A new experimental setup consisting of the HORUS array in combination with a double-sided silicon strip detector (DSSSD) was commissioned to allow for detailed particle-gated γγ-spectroscopy. The existing high-spin level-schemes of 137Nd, 137Ba, 136Ba, 135Ba, 134Ba, 133Ba, 133Xe, 131Xe, and 130I were substantially extended, emphasizing the transitional character of these odd-, and even-mass nuclei. The observation of distinct backbendings in 131Xe and 134Ba establishes an important link in the smooth evolution from spherical to deformed shapes. The identification of new positive- and negative-parity level structures in 136Ba and 137Ba indicates a sudden change of the structure of high-spin states along the N=80 and N=81 chains, only two and one neutrons outside the fully occupied neutron shell. Different high-spin members of the mixed proton-neutron π(g7/2)/(d5/2)⊗νh11/2 and πh11/2⊗νh11/2 configurations were identified in doubly-odd 130I. Moreover, a millisecond pulsing system at the FN tandem accelerator was commissioned during this thesis. The 2107-, and 2388-keV states in the 133Xe and 135Ba isotones were identified as millisecond Jπ= 23/2+ isomers, closing the systematic towards the recently investigated Jπ=23/2+ isomer in 139Nd. In addition, a comprehensive search for the anticipated Jπ=23/2+ isomer in 137Ce was performed using two different experimental approaches. A hitherto tentatively assigned isomer at 1942 keV in the N=77 isotone 133Ba was confirmed as a Jπ=19/2+ isomer with a newly measured half-life of T1/2=66.6(20) ns. Similarly, the half-life value of the Jπ=19/2+ isomer at 2222 keV in 137Nd was significantly improved with a new value of T1/2=0.38(7) ns. The obtained data close systematic gaps along isotopic and isotonic chains and improve the understanding of nuclear configurations nearby the doubly-magic 132Sn. Finally, new developments and recent theoretical advances in shell-model calculations are available for a refined systematic comparison in A≈130 nuclei. Present-day shell-model interactions like GCN50:82, Realistic SM, and PQM130 are capable to overcome the previous limitations of shell-model calculations. The predictions of these calculations are in good accordance with the new experimental findings and provide access into a detailed microscopic description of high-spin features and the gradual change of nuclear structure towards the shell closure at N=82
