Athens International Airport - Passport control
If you are an Eu citizen traveling inside the Schengen zone you do not have to pass through Passport control. However, you have to make sure that you carry a valid document defined by the national regulations of the Schengen states for determining your identity (a passport or ID card) when travelling. 
The countries that joined the Schengen Treaty are the following: Austria, Belgium, Bulgaria, Croatia, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Italy, Latvia, Liechtenstein, Lithuania, Luxemburg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland.
If you are travelling to/from a non-Schengen country, you will pass through Passport Control.
Passport control points
Passport Control points at Athens International Airport are operated by officers of the Hellenic Police who are entitled of verifying the authenticity of the travel documents presented by checking national & international databases. 
There are two flows dividing 
"European Union- EU passports/ ID holders " and 
"Non-Eu Passports holders".
If you are a biometric passport holder, passing through the Main Terminal Building, you may use the Eu “e-Passport” control points, which are automatic self-service border checkpoints.
(Biometric passport/e-passport is the one that contains a microchip & has the biometric symbol on the front cover).
You can use this system if you:
are a national of one of the EU countries, a national of an EEA country (Iceland, Liechtenstein, Norway) or Swiss national.
you are over 12 years old
You can use e-Passport control without prior registration.
There are instructions at each e-gate that help you pass smoothly. 
If these do not apply to you, or if you would prefer to be checked by a Police officer, you can still use the staffed counters at passport control.
Advice that will help you pass through quicker:
Please remove hats and sunglasses.
Have your passport open at the photo page and remove any holders or covers.
Useful information about entry requirements:
Please find out about the entry requirements from your airline, travel agent or the consulate/ embassy of your destination when planning your trip.
Before you travel, check that your passport, identity card and any visas you may need are still valid. Some countries require that your passport remain valid for a certain period after arrival. Immigration officials may also request additional documents such as a letter of invitation, evidence that you have booked accommodations, or proof that you have arranged onward or return transportation.
You can also enquire about the entry requirements for your destination at the International Air Transport Association (IATA) travel center.
Information about entry requirements can be found also on the website of the Hellenic Ministry of Foreign Affairs
If you are travelling from Greece to the United States or Canada, you need permission to travel in the form of an ESTA (US) or eTA (Canada). You must apply for this at least 72 hours before departure.
Travel to the UK
As of October 2021, it is no longer possible to enter the UK with an identity card, you must ensure that you have a valid passport.