Let \(\mathcal A\) be an affine plane, \(\overline {\mathcal A}\) its projective extension, and \(W\) the line at infinity. Choose a non-trivial subset \(D \subset W\), and denote by \({\mathcal G}_D\) the set of all lines intersecting \(W\) in a point of~\(D\), by \({\mathcal B}_D\) the set of all Baer subplanes whose line at infinity consists exactly of the points in~\(D\). Interchanging the sets \({\mathcal G}_D\) and \({\mathcal B}_D\) often yields a affine plane \(\mathcal A'\), the derived plane with respect to \(D\). Note that \(\mathcal A\) and \(\mathcal A'\) have the same point set \(A\), and that \(\mathcal A'' = \mathcal A\). Derivation in this sense has turned out to be a most fruitful idea for constructing interesting new planes. If \(\mathcal A\) is derivable, then, according to \textit{N. L. Johnson} [Abh. Math. Semin. Univ. Hamb. 58, 245-253 (1988; Zbl 0686.51002)], the incidence structure \({\mathcal S} = ({\mathcal G}_D, A ,{\mathcal B}_D)\) is isomorphic to the geometry \({\mathcal P}_S\) obtained from a projective space \({\mathcal P} = \text{PG}_3 F\) by deleting some line \(S\) with all of its points, all lines intersecting \(S\), and all planes containing \(S\). The author uses this observation to prove some general results on derivable affine planes. Among other things, he shows that the translation group of such a plane is isomorphic to a subgroup of the additive group of a vector space, and he characterizes those derivable translation planes which can be obtained by reversion of reguli. The second half of the paper deals with derivable planes admitting an affine Hughes group, i.e. a group \(\Theta\) of collineations of the affine plane which leaves some Baer subplane \({\mathcal Q} \cong \text{AG}_2F\) invariant and induces on \(\mathcal Q\) a group containing all translations as well as a group \(\text{ SL}_2F\). Affine Hughes groups have first been studied in the case \(F= \mathbb{R}\) by \textit{R. Löwen} [Forum Math. 10, No.~4, 435-451 (1998; Zbl 0914.51014)]. In the case that \(F\) is commutative and \({\mathcal Q} \in {\mathcal B}_D\), the author gives an explicit description of such planes in terms of a family of transversal mappings of \(F^2\).