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Let \( G \) be a Hamiltonian graph of order \( n \geq 3 \). For an integer \(\ell\) with \(1 \leq \ell \leq n\), the graph \( G \) is \(\ell\)-path-Hamiltonian if every path of order \(\ell\) lies on a Hamiltonian cycle in \( G \). The Hamiltonian cycle extension number of \( G \) is the maximum positive integer \(\ell\) for which every path of order \(\ell\) or less lies on a Hamiltonian cycle of \( G \). For an integer \(\ell\) with \(2 \leq \ell \leq n-1\), the graph \( G \) is \(\ell\)-path-pancyclic if every path of order \(\ell\) in \( G \) lies on a cycle of every length from \(\ell+1\) to \(n\). (Thus, a \(2\)-path-pancyclic graph is edge-pancyclic.) A graph \( G \) of order \( n \geq 3 \) is path-pancyclic if \( G \) is \(\ell\)-path-pancyclic for each integer \(\ell\) with \(2 \leq \ell \leq n-1\). In this paper, we present a brief survey of known results on these two parameters and investigate the \(\ell\)-path-Hamiltonian graphs and \(\ell\)-path-pancyclic graphs having small minimum degree and small values of \(\ell\). Furthermore, highly path-pancyclic graphs are characterized and several well-known classes of \(2\)-path-pancyclic graphs are determined. The relationship among these two parameters and other well-known Hamiltonian parameters is investigated along with some open questions in this area of research.