  We highlight intriguing features of complex networks that are grown by
\emph{redirection}. In this mechanism, a target node is chosen uniformly at
random from the pre-existing network nodes and the new node attaches either to
this initial target or to a neighbor of this target. This exceedingly simple
algorithm generates preferential attachment networks in an algorithmic time
that is linear in the number of network nodes $N$. Even though preferential
attachment ostensibly requires \emph{global knowledge} of the network,
redirection requires only \emph{local knowledge}. We also show that changing
just a \emph{single} attachment rate in linear preferential attachment leads to
a non-universal degree distribution. Finally, we present unexpected
consequences of redirection in networks with undirected links, where highly
modular and non-sparse networks arise.
