Above : Lunfthansa  Airplane
Most of International flights land in Tehran at the new Imam Khomeini International Airport or IK  based 37 km southwest of Tehran  and  Shiraz  city.

Iranian Airlines :
Iran Air ( Flag Carrier )
Mahan Air
Aseman Airlines

Non Iranian Airlines that operates  flights to Iran cities :
Lufthansa
KLM
Turkish Airlines
Air Pegasus
Qatar Airways
Aeroflot
Air Asia
Alitalia

Flights which  are operated by Iran Air, Iran Aseman Airlines, Mahan Air and other Iranian companies,  Fares  are  relatively cheap on  Iranian carriers.
Dubai  has scheduled flights to many Iranian cities, including Teheran , Shiraz   etc.  and  is  therefore  worth  considering  traveling to  Iran .
Iran Air and Mahan Air connect Tehran with some of the major European cities as well as destinations in Asia and Middle East.
European Airlines  have flights to  Tehran and  Shiraz  such as Lufthansa, KLM, Turkish Airlines, Alitalia, Aeroflot and Middle-Eastern airlines such as Qatar Airways.
Qatar Airways and  Mahan Air also has flights to/from Kuala Lumpur  to  Shiraz  (Recommended  for Australian travelers) Qatar Airways with  a  connection  in  Doha  but  Mahan Air  with a  direct  rout  lands in Shiraz . 
So finding a flight to Iran should not be hard.  (for the update Schedules you should  search via Airliners  Official  websites  or   ask your nearest Travel agency in your town)
    
 Mahan Air  has flights to Shiraz and Tehran  from  South east Asia.
 Iran Air  has  Flights to Tehran  from many European Capitals.
 Lufthansa has flights to Tehran, Ik airport
 KLM   has  Flights to Tehran  from many European Capitals.       
 Turkish Airlines has flights  to  Shiraz and other cities in Iran via  Istanbul  from many  European  Cities and  Washington DC.
Air Asia has  flights to Tehran  via  Kuala Lumpur  .
Qatar Air ways has flights to Shiraz from many destinations in Australia - Asia - USA
Air Pegasus  has flights to Iran from European cities which offers very cheap prices
Alitalia  has flights to Tehran airport
Aeroflot has flights to Tehran  airport  from Moscow and other departures
In case  of   flying  to  Shiraz, Iranian  Airliners  from  Kualalampur  have direct flight  to Shiraz  such  as  Mahan air. and from European countries Turkish airline and Qatar airways are the best options. 
Among  Iranian  based  airlines  Iran Air, Mahan Air and Aseman Airlines have been completely safe with no serious incidents during recent years. The service and flying skill of Iranian  pilots are fairly well known .
Due to sanctions there are no direct flights at present from Canada or the USA, but you could travel via either  Europe  or Persian  Gulf  States.  Non-stop flights  from Dubai  via   JFK, IAD, San Francisco, Los Angeles, Houston or Toronto are good bets. 
Travelers from Australia  or  New Zealand  can  consider  traveling via  Doha  or  Abu Dhabi  to  Shiraz  such as  Qatar  airways  or  Emirates, Al-Etihad  or  Air Arabia   or  through  Kuala take the direct flights to Shiraz .