  Exploration of the transient Universe is an exciting and fast-emerging area
within radio astronomy. Known transient phenomena range in time scales from
sub-nanoseconds to years or longer, thus spanning a huge range in time domain
and hinting a rich diversity in their underlying physical processes. Transient
phenomena are likely locations of explosive or dynamic events and they offer
tremendous potential to uncover new physics and astrophysics. A number of
upcoming next-generation radio facilities and recent advances in computing and
instrumentation have provided a much needed impetus for this field which has
remained a relatively uncharted territory for the past several decades. In this
paper we focus mainly on the class of phenomena that occur on very short time
scales (i.e. from $\sim$ milliseconds to $\sim$ nanoseconds), known as {\it
fast transients}, the detections of which involve considerable signal
processing and data management challenges, given the high time and frequency
resolutions required in their explorations, the role of propagation effects to
be considered and a multitude of deleterious effects due to radio frequency
interference. We will describe the techniques, strategies and challenges
involved in their detections and review the world-wide efforts currently under
way, both through scientific discoveries enabled by the ongoing large-scale
surveys at Parkes and Arecibo, as well as technical developments involving the
exploratory use of multi-element array instruments such as VLBA and GMRT. Such
developments will undoubtedly provide valuable inputs as next-generation arrays
such as LOFAR and ASKAP are designed and commissioned. With their wider fields
of view and higher sensitivities, these instruments, and eventually the SKA,
hold great potential to revolutionise this relatively nascent field, thereby
opening up exciting new science avenues in astrophysics.
