The formation of stripes in layered cuprate high-Tc superconductors and closely related nickelate compounds is generic. Doped charge carriers condense into spontaneously generated anti-phase domain walls between antiferromagnetic insulating regions. In this thesis fluctuations of spin and charge in these two-dimensional stripe superstructures are investigated. The first part addresses the phenomenon of spin-charge separation. Experimentally charge ordering of stripes is always observed at a higher temperature than the magnetic ordering. The melting of stripes mediated by the unbinding of different types of topological defects, namely charge dislocations, charge loops, and spin vortices is studied. The phase diagram and the critical properties of the phase transitions are calculated in the framework of a renormalization-group analysis in the Coulomb-gas representation of these defects, which interact logarithmically on large scales in two dimensions. Depending on which type of defect proliferates we identify four different phases characterized by the range of charge order, spin order, and a less accessible collinear order. From the resulting phase diagram several scenarios of spin-charge separation are possible. Depending on the interaction parameters the orders can disappear at a single transition or in a sequence of two transitions. In the second part the spin dynamics of stripes is studied in the framework of a linear spin-wave theory for a minimalistic spin-only model. The magnon dispersion and the magnetic zero temperature structure factor are calculated for diagonal and vertical stripes since both configurations are realized in doped layered antiferromagnets. Acoustical as well as optical bands are included in the analysis. Incommensurate spin fluctuations and the commensurate pi-resonance at the antiferromagnetic wave vector appear as complementary features of the band structure at different energy scales. The dependence of the spin-wave velocities and the resonance frequencies on the stripe spacing and coupling is calculated. At low doping, the resonance frequency is found to scale inversely proportional to the stripe spacing. Finally, we extend our minimalistic model to a bilayer, allowing for several stripe configurations which differ by the relative location of the stripes in the layers. Again the spectral properties are calculated in linear spin-wave theory. We focus on the bilayer splitting of the magnon bands near the incommensurate low energy peaks as well as near the pi- resonance, distinguishing between the odd and even channel. We find that an x-shaped dispersion near the pi-resonance is generic for stripes. The favorable comparison of the results to experimental data suggests that the spin-only model provides a suitable and simple basis for calculating and understanding the spin dynamics of stripe
