Hey everyone,
At my company in the US all of our travel on our own airline in by e-ticket. That includes travel by the employee, eligible family, domestic partners, and companions. The employee must list the traveler by internet, automated telephone, or company system. That person may check in at the automated machines at the airport when they are available. Charges are deducted automaticaly from our paychecks. It is quite a slick system comparted to that of years ago.
Travel on other airlines (few offer zed fares) must be ticketed by our company by telephone call and mail, or airport pick up (usually crowded). We may charge these tickets to credit cards and then get unused tickets refunded (another long airport wait or risk of mailing).
If you have any more questions, I'll be glad to answer.
Take care!