  We consider the possibility of multiply-connected spacetimes, ranging from
the Flamm-Einstein-Rosen bridge, geons, and the modern renaissance of
traversable wormholes. A fundamental property in wormhole physics is the
flaring-out condition of the throat, which through the Einstein field equation
entails the violation of the null energy condition. In the context of modified
theories of gravity, it has also been shown that the normal matter can be
imposed to satisfy the energy conditions, and it is the higher order curvature
terms, interpreted as a gravitational fluid, that sustain these non-standard
wormhole geometries, fundamentally different from their counterparts in general
relativity. We explore interesting features of these geometries, in particular,
the physical properties and characteristics of these `exotic spacetimes'.
