  One of the fundamental rules of nature and a pillar in the foundation of
quantum theory and thus of modern physics is represented by the Pauli Exclusion
Principle. We know that this principle is extremely well fulfilled due to many
observations. Numerous experiments were performed to search for tiny violation
of this rule in various systems. The experiment VIP at the Gran Sasso
underground laboratory is searching for possible small violations of the Pauli
Exclusion Principle for electrons leading to forbidden X-ray transitions in
copper atoms. VIP is aiming at a test of the Pauli Exclusion Principle for
electrons with high accuracy, down to the level of 10$^{-29}$ - 10$^{-30}$,
thus improving the previous limit by 3-4 orders of magnitude. The experimental
method, results obtained so far and new developments within VIP2 (follow-up
experiment at Gran Sasso, in preparation) to further increase the precision by
2 orders of magnitude will be presented.
