  We prove two dichotomy results for detecting long paths as patterns in a
given graph. The NP-hard problem Longest Induced Path is to determine the
longest induced path in a graph. The NP-hard problem Longest Path
Contractibility is to determine the longest path to which a graph can be
contracted to. By combining known results with new results we completely
classify the computational complexity of both problems for $H$-free graphs. Our
main focus is on the second problem, for which we design a general
contractibility technique that enables us to reduce the problem to a matching
problem.
