Zagreb, Croatia's capital is the main entry point into the country. You'll find plenty of flights to Zagreb from all European capitals run by Croatia Airlines the national carrier, as well as other airlines. Year-round there's a London-Heathrow to Zagreb flight by British Airways.
Lately more air routes to Croatia have been opening up and there are good deals on direct flights to other Croatian gateway cities such as Dubrovnik, Pula, Split and Zadar as well as flights to Zagreb.
Low-cost carriers such as Ryanair, Volotea and Easyjet have introduced many summer flights to Croatia.
Notice that the only direct flights from North America are New York (Newark) to Dubrovnik with United Airlines and Toronto to Zagreb with Air Transat.
Otherwise, the best deals on a round trip flight to Zagreb will involve at least one change in Europe. You may be tempted to fly to London to take advantage of a cheap fare to the Croatian coast. Be aware that some low-cost airlines to Croatia are not flying out of international airports such as Heathrow or Gatwick but use the local airports, Stansted, City or Luton.
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Below is a list of low-cost airlines with routes to Croatia this year along with the launch dates.