When considering your flights from the US to Europe and back, they will more than likely be Round Trip.

Round Trip Example

Round Trip flights mean your original departure point will also be your final return point and your destination will also be your point of departure on your return.

Some airlines may offer an optional Stopover either inbound or outbound but not both for no additional charge.  For example, flying from Denver to Frankfurt on Iceland Air, they offer either an inbound or outbound stop in Reykjavik Iceland at no additional charge for up to a 7 night stay.

Round Trip flights may sometimes be cheaper but not in all cases.  When purchasing your flights, consider where you want to go and what you plan to see and do.  If you are planning on visiting different locations separated by a great distances where you will travel by train or air, you may want to consider something like the Destination Open Jaw described below opposed to wasting time and money returning back to your original arrival point just to fly home.

Compare the costs of the Round Trips, Open Jaws and other transportation that may be required.

Origin Open Jaw Example

These are flights departing from location (LHR) arriving at location (CDG) then departing location (CDG) returning to a different location (MAN).

Destination Open Jaw Example

These are flights departing from location (LHR) arriving at location (SYD) then departing a different location (BNE) returning to the same location (LHR).

Point-to-Point

These are flights departing from (LHR) arriving at (SYD) then later departing from a different location (BNE) returning to a different location (MAN)

As train travel is so convenient in Europe, consider the Destination Open Jaw where you will arrive in Europe at one location and return from another.  For example, you may fly into Paris France then take a high speed train to Lion France before heading via train to Geneva Switzerland for several days.  It does not make sense to waste time and money returning all the way back to Paris when you could simply fly back from Geneva.

Europe has several Low Cost Carriers such as Ryan Air offering inexpensive flights throughout Europe.  These Low Cost Carriers may or may not fly out of the major airports in all countries.  For example, you would not be flying Ryan Air from London Heathrow but more likely from Stansted, Luton or Gatwick.  When you are planning your trip, consider other flights around Europe if you are not traveling by train.