With a little planning, you can get through the airport security bottleneck without issue. Remember that you can bring baby formula, pumped breast milk and juice through security, but in many countries, water and other liquids are limited. Plan to buy bottled water after you've passed through security.
A baby sling can be especially helpful at this point. It leaves your hands free for maneuvering luggage and removing your shoes.
If you've decided to hold your baby rather than reserve a seat, the infant still needs a boarding verification document when passing through security. Some airlines let you take your stroller to the gate, where it will become checked luggage and you can retrieve it when getting off the plane.
At no time should you be separated from your baby during the security check. And just a reminder: Never put your baby through the X-ray machine (yes, it has happened).