Exstensible monadic exceptions.
Extensible exceptions are a good solution to the exception problem in Haskell. However, there is one problem: they are not extensible enough! The problem is that the functions defined in Control.Exception for dealing with exceptions can only be used with the IO monad. A lot of Haskell code uses a stack of monads, at the bottom of which is IO, but the IO monad is not used directly.
There have been many attempts to solve this problem, but the stumbling block has been the presence of short-circuiting monad transformers: sometimes, these prevented the cleanup actions from being run, making it effectively impossible to catch exceptions in such monads. The monad-control package has been developed as a solution to this problem: it defines a way to turn a monad transformer stack "inside-out", which ensures that cleanup actions are run even when the original action short-circuits. The lifted-base package, built on top of monad-control, exports the Control.Exception.Lifted module, which contains versions of the Control.Exception functions that work on any monad stack with IO at its base.
This has pretty much solved the above problems. However, one thing that the solutions that came before monad-control did was provide a type class encapsulating exception functionality that could be implemented by pure monads, allowing you to use the same interface to throw and catch exceptions in both pure and IO-based code. This also makes it possible to express which can throw an exception, but which don't necessarily do any IO and which are polymorphic in their exception throwing (i.e., you could run the function in IO and it would use throwIO, or you could run it as an Either and it would use Left).
That's what this package does. It provides a MonadException type class (in the Control.Monad.Exception.Class module), which has instances for IO and IO-like monads (for which monad-control is used to provide the correct instances as described above), as well as for some pure monads. Several overlapping instances (in the spirit of mtl-evil-instances) are provided, so it is not necessary to provide a pass-through instance for MonadException for every monad transformer you write.
This package also defines an ExceptionT monad transformer (in Control.Monad.Trans.Exception) that can be used to add MonadException functionality to otherwise pure monad stacks. mtl-evil-instances is used to automatically provide pass-through instances for the mtl type classes for this transformer.
Finally, this package includes the module Control.Exception.Monadic, which is a full replacement for Control.Exception, whose functions work on any instance of MonadException and not just IO. The functions for dealing with asynchronous exceptions require IO however, so these are only polymorphic for any IO-like monadic (as determined by monad-control).