Terrorism imposes a challenge for global se curity and is spread worldwide. At the same time, it is also a national problem and is anticipated in national criminal codes as a criminal offence. This is due tosignificant geopolitical events and global social changes. Nowadays, terrorism is aglobal threat, it is new, more deadly, expressed in its refined magnitude, destructivity and professionally coordinated attack planning; Ieanton the most advanced technology of the modern civilization; led by international non-state organizations throughthe global network of terrorist organizations that are located in many countries; associated with fanatic extremists; based on a principle that destruction power is equal to the power of change and control; and urged by the hatred towards the target, by the wish to see its target suffering because of what the target represents and what values it is fighting for. As such, terrorisam has also been present in Bosnia and Herzegovina. Many factors imply its presence: terrorist attacks, training of potential terrorists, planning and preparation of terrorist attacks (courtverdicts), presence of certain terrorist groups/cells, etc. This kind of terrorism requires an adequate response which should be globe - wide. Bosna and Hercegovina should take a participation in the response through certain institutional and criminal justice regulations, at the same time respecting human rights and freedoms.