  We investigate the role of gentle algebras in higher homological algebra. In
the first part of the paper, we show that if the module category of a gentle
algebra $\Lambda$ contains a $d$-cluster tilting subcategory for some $d \geq
2$, then $\Lambda$ is a radical square zero Nakayama algebra. This gives a
complete classification of weakly $d$-representation finite gentle algebras. In
the second part, we use a geometric model of the derived category to prove a
similar result in the triangulated setup. More precisely, we show that if
$\mathcal{D}^b(\Lambda)$ contains a $d$-cluster tilting subcategory that is
closed under $[d]$, then $\Lambda$ is derived equivalent to an algebra of
Dynkin type $A$. Furthermore, our approach gives a geometric characterization
of all $d$-cluster tilting subcategories of $\mathcal{D}^b(\Lambda)$ that are
closed under $[d]$.
