The frequency of acts of violence in the world has increased in recent years. These acts, perpetuated by different groups under different guises, have one thing in common: the invocation of a sense of terror and horror in people. In Africa, the situation is the same. Events in countries in and around the Horn of Africa, East Africa, Mali, Kenya and Nigeria, to name a few, speak to the rise in events of this nature that leave a trail of loss of life and property and destruction in their wake. At regional and continental levels, different initiatives, both legal and military, have been put in place all over the world to deal with acts of terrorism, and the perpetrators thereof. Despite these, terrorist attacks continue to happen unabated. It is questionable if these initiatives are achieving the desired results, and if these are indeed the correct measures to apply to tackle the malaise. Hence, this paper seeks to examine the nature and peculiarities of the terrorism occurring in Africa, focusing particularly on the groups al-Shabaab in the Horn of Africa, and Boko Haram in West Africa. The effectiveness of current efforts at combatting terrorism is examined with a view to recommending a more nuanced approach to the battle against terrorism in Africa.