  (abridged) Magnetic reconnection is the topological reconfiguration of the
magnetic field in a plasma, accompanied by the violent release of energy and
particle acceleration. Reconnection is as ubiquitous as plasmas themselves,
with solar flares perhaps the most popular example. Over the last few years,
the theoretical understanding of magnetic reconnection in large-scale fluid
systems has undergone a major paradigm shift. The steady-state model of
reconnection described by the famous Sweet-Parker (SP) theory, which dominated
the field for ~50 years, has been replaced with an essentially time-dependent,
bursty picture of the reconnection layer, dominated by the continuous formation
and ejection of multiple secondary islands (plasmoids). Whereas in the SP model
reconnection was predicted to be slow, a major implication of this new paradigm
is that reconnection in fluid systems is fast (i.e., independent of the
Lundquist number), provided that the system is large enough. This conceptual
shift hinges on the realization that SP-like current layers are violently
unstable to the plasmoid instability - implying, therefore, that such current
sheets are super-critically unstable and thus can never form in the first
place. This suggests that the formation of a current sheet and the subsequent
reconnection process cannot be decoupled, as is commonly assumed. This paper
provides an introductory-level overview of the recent developments in
reconnection theory and simulations that led to this essentially new framework.
We briefly discuss the role played by the plasmoid instability in selected
applications, and describe some of the outstanding challenges that remain at
the frontier of this subject. Amongst these are the analytical and numerical
extension of the plasmoid instability to (i) 3D and (ii) non-MHD regimes. New
results are reported in both cases.
