The rotational evolution of pulsars reveals deviations from simple spin-down models, most notably in the form of "pulsar glitches" - sudden increases in spin frequency - and "timing noise", a low-frequency stochastic wandering of the pulsar's rotation around its spin-down trend. Both phenomena are believed to arise from the dynamics of superfluid components in the stellar interior. In particular, the presence of quantised vortices, which mediate angular momentum transport in neutron star interiors, introduces complex, non-linear behaviour capable of producing both discrete and continuous spin irregularities.

I will present recent developments in simulating the dynamics of these quantised vortices and their interactions with the solid crust of the neutron star. Such simulations offer valuable insight into the mechanisms through which superfluid angular momentum is stored and released, giving rise to observable features like glitches and long-term timing noise.