  Born-Infeld theory admits finite energy point particle solutions with
$\delta$-function sources, BIons. I discuss their role in the theory of
Dirichlet $p$-branes as the ends of strings intersecting the brane when the
effects of gravity are ignored. There are also topologically non-trivial
electrically neutral catenoidal solutions looking like two $p$-branes joined by
a throat. The general solution is a non-singular deformation of the catenoid if
the charge is not too large and a singular deformation of the BIon solution for
charges above that limit. The intermediate solution is BPS and Coulomb-like.
Performing a duality rotation we obtain monopole solutions, the BPS limit being
a solution of the abelian Bogolmol'nyi equations. The situation closely
resembles that of sub and super extreme black-brane solutions of the
supergravity theories. I also show that certain special Lagrangian submanifolds
of ${\Bbb C}^p$, $p=3,4,5$, may be regarded as supersymmetric configurations
consisting of $p$-branes at angles joined by throats which are the sources of
global monopoles. Vortex solutions are also exhibited.
