Command and control

In North America and other continents, for a threatened or completed terrorist attack, the Incident Command System (ICS) is apt to be invoked to control the various services that may need to be involved in the response. ICS has varied levels of escalation, such as might be needed for multiple incidents in a given area (e.g., the 2005 bombings in London or the 2004 Madrid train bombings, or all the way to a National Response Plan invocation if national-level resources are needed. National response, for example, might be needed for a nuclear, biological, radiological, or large chemical attack.
Damage mitigation
Fire departments, perhaps supplemented by public works agencies, utility providers (e.g., gas, water, electricity), and heavy construction contractors, are most apt to deal with the physical consequences of an attack.
Local security
Again under an incident command model, local police can isolate the incident area, reducing confusion, and specialized police units can conduct tactical operations against terrorists, often using specialized counter-terrorist tactical units. Bringing in such units will normally involve civil or military authority beyond the local level.