Since the 9/11 attacks, large-scale terrorism has been occurring in various parts of the world.
Literal
9/11 terror [since-以来], world [genitive-の] each-place [at-で] large-scale [adjectival-な] terrorism [subject-が] has-been-occurring.
A news-summary sentence. ~以来 ('since X,' 'from X onward') is a formal temporal marker attached to a noun or a past-tense verb — 9.11テロ以来 = 'since the 9/11 terrorist attacks.' 各地 ('various places,' 'each place') is a productive 各 + [noun] compound for 'each X' or 'various X's' — 各国 (each country), 各種 (each kind), 各部 (each department). ~が発生している is the present progressive of 発生する ('to occur, arise') — 'has been occurring,' 'has been happening.' Marks the ongoing trend.