You'll have no trouble providing evidence for these claims then?
Sure. If you're happy with it, I will look at a couple of example groups.
Al-Qaeda Organization in the Islamic Maghreb
This organisation was formerly known as
Salafist Group for Preaching and Combat but probably known more commonly as GSPC. They are a radical islamic group with the stated aim of overthrowing the Algerian government and establishing an Islamic state.
The GSPC is a splinter group of the GIA, formed in 1998. In September 2006 Ayman al-Zawahri announced a "blessed union" between Al Qaeda and the GSPC and in January 2007 the group formally changed its name to Al Qaeda.
Here is a PDF by the Centre For Policing Terrorism which summarises the scope of GSPC. They have an extensive network in the Sahara and Europe, and their primary source of funding is criminal activity. As well as members being trained in Al Qaeda camps in Afghanistan, Libya has discovered GSPC training camps and it is believed they operate camps throughout the Sahara. This month it was reported that about 40 fighters at a GSPC training camp had contracted bubonic plague, although other sources claim it was a result of a chemical weapons accident.
Tanzim Qaidat al-Jihad fi Bilad al-Rafidayn
(Al Qaeda in Iraq)
This organisation was formerly known as Jama'at al-Tawhid wal-Jihad and was created by Jordanian Abu Musab al-Zarqawi following the Soviet-Afghanistan War. Although it initially had the goal of overthrowing the Jordanian kingdom, the group became an international one as the network expanded. The group has always had close ties to Al Qaeda (they ran an Al Qaeda training camp near Herat in Afghanistan) and in October 2004 they officially swore allegiance to Osama Bin Laden.
This PDF by the Congressional Research Service provides an insight into the operation of this organisation. Of particular note is the section on foreign fighters which addresses the organisation's networks for channelling foreign fighters into Iraq.
Again, none of this should be surprising. These Radical Islamic groups have a long history of establishing comprehensive funding networks, and of bringing in fighters from across the Arab world to be trained, and to fight. They did it in the Soviet-Afghanistan War, they did it in Chechnya and Bosnia, and there's no reason to assume they're not doing it now, particularly given the evidence they are.
Regular old-fashioned police work seems to be keeping it under control, for a value of "under control" consistent with terrorism being far less of a threat to the average citizen's wellbeing than traffic accidents or doughnuts.
The mere fact that you think the problem is terrorist attacks is a prime example of just how out of touch with reality the west is, when it comes to the nature of this threat. Terrorist attacks are only one small part of their tactics. When the British government are publicly endorsing and praising Radical Islamic mosques that are promoting extremism, and when the British Government is openly supporting groups that are secretly funneling fighters into Afghanistan, I'm sorry but the situation is most certainly not "under control". It's even less under control when the country providing most of the funds for this spread of radical ideology is considered a strong western ally.
And let's not forget, the role of terrorism is not to try and kill people. It's to force change. And evidence of those changes is available wherever you might look for it. Can you claim Spanish police have Islamic Terrorism "under control" if a terrorist bombing can dictate Spanish foreign policy?