Aiming towards largely integrated quantum bits (qubits) requires the development of solid-state, two-level quantum systems, such as spins in quantum dots or Majorana fermions in one-dimensional wires. Holes confined in low-dimensional, germanium-based heterostructures are good candidates for such qubits because they offer i) large spin-orbit interaction (SOI), leading to conveniently large g factors, ii) reduced hyperfine coupling, which is important for long spin coherence, and iii) relatively low effective masses, favoring quantum confinement. In this thesis, I have investigated hole transport in one- and two-dimensional systems made from compressively strained Ge/Si_0.2Ge_0.8 heterostructures. An important part of my research work has been devoted to developing the recipes for device fabrication. I have started from the fabrication of gated Hall bar devices from nominally undoped Ge/SiGe heterostructures. I have studied two types of the heterostructures embedding a strained Ge quantum well: one where the Ge well is at the surface, hence easily accessible to metal contacts, and one where it is buried 70 nm below the surface, a configuration resulting in higher hole mobility. The electronic properties of the two-dimensional hole gas confined to the Ge well were studied by means of magneto-transport measurements down to 0.3 K. My measurements revealed a dominant heavy-hole character, which is expected from the presence of a compressive strain in combination with two-dimensional confinement. The surface-Ge devices showed diffusive transport and a weak anti-localization effect, which is due to SOI in combination with quantum interference. The fact that the Ge quantum well is located at the surface allows for relatively large perpendicular electric fields and hence enhanced Rashba-type SOI. I was able to estimate a spin splitting of around 1 meV. For the realization of quantum nano-devices, I used the heterostructure with a buried Ge well where the hole mobility approaches 2×105 cm2/Vs. Using e-beam lithography, sub-micron metal gates were defined on sample surface in order to create one-dimensional constrictions in the two-dimensional hole gas. I succeeded in observing conductance quantization in hole quantum wires with a length up to ~ 600 nm. In these wires I investigated the Zeeman splitting of the one-dimensional subbands, finding large perpendicular g-factors as opposed to small in-plane g-factors. This strong anisotropy indicates a prevailing heavy-hole character, which is expected in the case of a dominant confinement in the perpendicular direction. The large g factors and the ballistic one-dimensional character are favorable properties for the realization of Majorana fermions. Finally, I have begun to explore the potential of Ge-based heterostructures for the realization of quantum-dot devices, having in mind applications in spin-based quantum computing. During the last months, I was able to observe clear evidence of single-hole transport, laying the ground for more in-depth studies of hole quantum dots.