  Given a graph $G$ with source and destination vertices $s,t\in V(G)$
respectively, \textsc{Tracking Paths} asks for a minimum set of vertices
$T\subseteq V(G)$, such that the sequence of vertices encountered in each
simple path from $s$ to $t$ is unique. The problem was proven \textsc{NP}-hard
\cite{tr-j} and was found to admit a quadratic kernel when parameterized by the
size of the desired solution \cite{quadratic}. Following recent trends, for the
first time, we study \textsc{Tracking Paths} with respect to structural
parameters of the input graph, parameters that measure how far the input graph
is, from an easy instance. We prove that \textsc{Tracking Paths} admits
fixed-parameter tractable (\textsc{FPT}) algorithms when parameterized by the
size of vertex cover, and the size of cluster vertex deletion set for the input
graph.
