The present work contains two parts, both devoted to the investigation of light nuclei. In the first part of the thesis the structure of the exotic 7He nucleus is studied. The disappearance of the usual magic numbers in extremely neutron-rich nuclei implies a considerable modifcation in the spin-orbit interaction. Recent experiments yield contradictory results about a possible existence of the p1/2- spin-orbit partner of the 7He ground state with a dominant p3/2- single-particle character. In order to clarify this question a study of the 7Li(d,2He)7He reaction has been performed using a 171 MeV deuteron beam provided by the cyclotron at Kernfysisch Versneller Insituut (KVI) in Groningen. The experiment was carried out in April 2003. The setup at KVI offers a resolution ΔE ≈ 150 keV (FWHM) in the measured spectra, better than the line width of the ground state of 7He. The unbound 2He system was identifed by detecting coincidences between two protons with small relative energy. The data were taken over the angular range Θ_cm = 0…11.3 deg. A possible resonance at an excitation energy Ex = (1.45 +0.7 -0.5) MeV with a width Γ = (2.0 +1.0 -1.1) MeV is suggested by a decomposition of the spectrum using known resonances, the breakup behaviour of 7He and quasifree charge-exchange contributions, taking into account the cluster structure of 7Li. Gamow-Teller strengths for transitions to the lowest states in 7He are in remarkable agreement with results from ab initio Quantum Monte Carlo calculations. The neutron spectroscopic factor Sn = 0.64 +/- 0.09 of the 7He ground state (7He = 6He+n) is extracted by an R-matrix analysis. In the second part of the thesis the deuteron breakup has been studied in the 2H(e,e’) reaction at Θ = 180 deg. The present measurements were performed in March and April 2006 at the superconducting Darmstadt electron linear accelerator S-DALINAC at an incident electron energy E0 = 27.8 MeV and 74 MeV. At low momentum transfer (q = 0.28 fm-1 and 0.73 fm-1, respectively) magnetic transitions are expected to give the dominant contributions to the breakup cross sections. Thus, the measured deuteron-electrodisintegration cross section at threshold can be used to obtain the cross section for the np →d γ reaction applying the principle of detailed balance. The accurate information about this process is of great interest in nuclear astrophysics, specifically with regard to Big-Bang nucleosynthesis. The experimental data are in excellent agreement with theoretical calculations based on a nucleon-nucleon potential model (Bonn-B), under the inclusion of meson-exchange and isobar effects.