  This review provides the background and current perspective of some of the
striking asymmetries exhibited by extragalactic double-lobed radio sources,
paying special attention to the reported interrelationships among some of them.
We particularly aim to highlight some less discussed aspects pertaining to the
radio lobes and hot-spots for which any relativistic beaming effects are milder
than those imposed on the jets. Various attributes of these features, such as
their geometry, intensity, spectrum, and polarization provide important
underpinnings to models of radio galaxies and quasars, as well as to theories
that attempt to unify them. These contraints are sharpened by exploiting the
asymmetry properties of the extended optical emission-line regions associated
with powerful radio sources, including the giant halos of Lyman-alpha emission
associated with them. We suggest that highly extended disks of dusty gaseous
material, which could also be parts of cosmic filaments, around the host
galaxies of radio sources may hold the key to understanding the correlated
radio--optical asymmetry and perhaps also the depolarization asymmetry of the
twin radio lobes. We also discuss the nature and possible implications of the
extreme type of asymmetry witnessed in the enigmatic quasar 3C273, whose entire
radio emission is observed on just one side of the nucleus. In this context,
theoretical scenarios for the production of one-sided jets are also briefly
recounted. Taking a clue from theobserved one-sidedness of the extended radio
jets even in `weak-headed-quasars', we also propose a scenario for the late
evolutionary stage of double radio sources. We end with a list of key questions
concerning radio source asymmetries which still require final answers.
(Abridged)
