||Weyl semimetals have been providing for a considerable research interest in the last decade in quantum condensed matter physics, due to their non-trivial topological nature and their possible applications in material science. Their non-trivial topological order has many consequences like zero energy Weyl nodes, which are robust to impurities and display a chiral anomaly. The work presented in this thesis is inspired by the intriguing matter of the response of Weyl semimetals to topological defects and their change to the behaviour of underlying lattice. To achieve this, we studied the response of different types of Weyl semimetals upon introducing a lattice dislocation or a pi-flux vortex, which mimics the effect of the former. Specifically, we show that the existence of a (or multiple) Kramers pair(s) of zero-energy modes bound to a dislocation line or vortex is a not a generic feature of topologically non-trivial phases of Weyl semimetals since this appears to depend on the present number of Weyl nodes and their chiralities as well as the type of symmetry breaking. We obtain the explicit form of these states, which shows their exponentially localised nature. Furthermore, we analyse the dependence of the energy of these dislocation modes on different parameters of the models and analyse the resulting correlations found. We then conclude by placing these results in a broader context.