  A laminar family is a collection $\mathscr{A}$ of subsets of a set $E$ such
that, for any two intersecting sets, one is contained in the other. For a
capacity function $c$ on $\mathscr{A}$, let $\mathscr{I}$ be $\{I:|I\cap A|
\leq c(A)\text{ for all $A\in\mathscr{A}$}\}$. Then $\mathscr{I}$ is the
collection of independent sets of a (laminar) matroid on $E$. We present a
method of compacting laminar presentations, characterize the class of laminar
matroids by their excluded minors, present a way to construct all laminar
matroids using basic operations, and compare the class of laminar matroids to
other well-known classes of matroids.
