Abstract Helium is the second most abundant element in the Universe. It is the only known substance that can exist in liquid state at absolute zero. There are two stable isotopes of helium, fermionic ³He and bosonic ⁴He. At sufficiently low temperatures, both isotopes undergo a phase transition into a superfluid state. These superfluids are usually characterised by their ability to flow without resistance, but this is by no means their only remarkable property. In this thesis, we study theoretically superfluid ³He. The work consists of two separate projects. First, we study the effect of a quantised vortex line to spin dynamics of the superfluid. We find that the interplay between the vortex and the magnetisation of the liquid generates spin waves, dissipating energy. We find that the theoretically predicted energy dissipation is in agreement with experimental data, implying that spin-wave radiation can be an important mechanism of magnetic relaxation in superfluid ³He. Second, we study the drag force acting on an object moving through zero-temperature superfluid at a constant velocity. The drag arises if momentum is transferred from the object to the fluid. At low velocities, no such mechanism exist and thus the drag vanishes. If the velocity exceeds the Landau velocity \(v_L\), it becomes possible for the object to create quasiparticle excitations that could, in principle, transfer momentum away from the object. Thus, \(v_L\) has been generally assumed to be the critical velocity, that is, the velocity above which the drag force starts to increase rapidly towards the normal-state value. We find that this is not necessarily the case. Objects much larger than the superfluid coherence length modify the superfluid flow field around them. The spatial variation of the flow field can shield the object, preventing quasiparticles from transferring momentum away from the object. This leads to a critical velocity greater than \(v_L\). / Original papers The original publications are not included in the electronic version of the dissertation. Laine, S. M., & Thuneberg, E. V. (2016). Calculation of Leggett–Takagi Relaxation in Vortices of Superfluid ³He-B. Journal of Low Temperature Physics, 183(3–4), 222–229. https://doi.org/10.1007/s10909-016-1516-x Kuorelahti, J. A., Laine, S. M., & Thuneberg, E. V. (2018). Models for supercritical motion in a superfluid Fermi liquid. Physical Review B, 98(14). https://doi.org/10.1103/physrevb.98.144512 http://jultika.oulu.fi/Record/nbnfi-fe2018112148794 Laine, S. M., & Thuneberg, E. V. (2018). Spin-wave radiation from vortices in ³He−B. Physical Review B, 98(17). https://doi.org/10.1103/PhysRevB.98.174516 http://jultika.oulu.fi/Record/nbnfi-fe2019092630083