Terrorism imposes a challenge for global security and is spread worldwide. At the same time, it is also a national problem and is identified in national criminal codes as a criminal offence. This is due to significant geopolitical events and global social changes. Nowadays, terrorism is a global threat, it is new, more deadly, expressed in its refined magnitude, destructivity and professionally coordinated planning of attacks; borrowing from the most advanced technology of modern civilization; led by international non-state organizations through the global network of terrorist organizations that are located in many countries; associated with fanatic extremists; based on a principle that destructive 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, terrorism 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 (court verdicts), presence of certain terrorist groups/cells, etc. This kind of terrorism requires an adequate response which should be global in nature. Bosna and Hercegovina should participate in the response through certain institutional and criminal justice regulations, at the same time respecting human rights and freedoms.