  Fix two points $p$ and $q$ in the plane and a positive number $k \neq 1$. A
result credited to Apollonius of Perga states that the set of points $x$ that
satisfy $d(x, p)/d(x, q) = k$ forms a circle. In this paper we study the
analogous set in taxicab geometry. We find that while Apollonian sets are not
taxicab circles, more complicated Apollonian sets can be characterized in terms
of simpler ones.
