  The codification in higher dimensional Hilbert Spaces (whose logical basis
states are dubbed qudits in analogy with bidimensional qubits) presents various
advantages both for Quantum Information applications and for studies on
Foundations of Quantum Mechanics.
  Purpose of this review is to introduce qudits, to summarize their application
to Quantum Communication and researches on Local Realism and, finally, to
describe some recent experiment for realizing them.
  A Little more in details: after a short introduction, we will consider the
advantages of testing local realism with qudits, discussing both the 3-4
dimensional case (both for maximally and non-maximally entanglement) and then
the extension to an arbitrary dimension. Afterwards, we will discuss the
theoretical results on using qudits for quantum communication, epitomizing the
outcomes on a larger security in Quantum Key Distribution protocols (again
considering separately qutrits, ququats and generalization to arbitrary
dimension). Finally, we will present the experiments performed up to now for
producing quantum optical qudits and their applications. In particular, we will
mention schemes based on interferometric set-ups, orbital angular momentum
entanglement and biphoton polarization. Finally, we will summarize what
hyperentanglement is and its applications.
