What are the requirements for the installation of fire and smoke dampers?

Any examples are for illustrative purposes only.
Generally, fire dampers are required where air ducts penetrate walls that are rated for 2-hours or more.  They are needed in all air transfer openings (non-ducted) in rated walls, regardless of the rating.  And they are required at some, but not all penetrations of rated floor assemblies and shaft enclosures. 

Smoke dampers are required at penetrations of smoke barriers, unless the HVAC system is fully ducted and there is a sprinkler system installed throughout the facility, in which case they are not required. Smoke dampers are also required in air transfer openings (non-ducted) in smoke partitions.

Where a penetration requires both a fire damper and a smoke damper, combination units that are both smoke responsive and heat responsive may be used. 

Reference LS.02.01.10 EP13, LS.02.01.30 EP22 & EP23