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Nowadays most airlines have loyalty programs. These frequent flyer programs mean that you can fly a specific airline and get miles, which you can subsequently use to pay for your tickets. Delta also has a loyalty program named Delta SkyMiles. Since 2015 the program is revenue-based, meaning that the number of miles earned depends not on the number of miles flown, but on the price on the ticket. Right now Delta values well off travelers more than actually frequent travelers. Delta has an elite status within SkyMiles program, called Medallion, which also affects your mileage accrual.
Generally, in order to earn frequent flyer miles on Delta and follow your status you need to register in the program online or get a co-branded credit card from American Express. After that you'll have access to booking and other actions with your account. Delta has an award calendar that shows you award prices for selected flights. It also has a search system, but it is notorious for being incredibly buggy, so in fact you are better off using Air France facilities.
Using miles earned from Amex cards or from registration in a program, you can book an award ticket online or over the phone. Note that award tickets don't mean free tickets, usually you pay additional fees like fuel surcharges. Besides, the cost of miles differs as well. You can determine the value of your miles if you divide the cash value of your ticket by the number of miles required for the flight. However, Delta SkyMiles are worth around 1.8 cents, more if redeemed for international business-class flights. You can't see exactly how many miles your ticket will bring you as Delta doesn't have an award chart anymore, but the general line is that within the US economy class tickets equal to 5,000-12,500 miles and business class - 25,000 while flying to Australia will give you 45,000 and 95,000 SkyMiles respectively.
Flying Delta, you not only get frequent flyer miles, but also get multiple opportunities to get Medallion status. It has for tiers: Silver Medallion, Gold Medallion and Platinum Medallion. Depending on the tier, Medallion status can give you complimentary upgrades, bonus miles, free checked bags, priority access and lounge access. To achieve Medallion status, you need to collect a number of Delta special currency: MQM, MQS or MQD. MQMs - Medallion Qualifying Miles - are miles that are given based on the distance flown. You can't spend them on award tickets, only collect to achieve Medallion status. MQSs - Medallion Qualifying Segments are earned depending on the number of segments you fly. Generally you get 1 MQS for a landing and takeoff. The rule of thumb is that you earn more MQMs for a small number of long flights, but more MQSs for a lot of short flights. MQDs - Medallion Qualifying Dollars - are a cashback system, you earn 1 MQD per 1 dollar spent.
You can use SkyMiles in a variety of options. The most obvious way is buying award tickets. The way to squeeze more value of your miles is to fly business class on international flights and economy on domestic flights. You can also get discounts on your tickets using Delta's program Pay with Miles, which allows you to redeem miles for a fixed value. As for Delta's partners, Delta is a member of SkyTeam alliance, so you can purchase tickets from one of Delta's partners. Have in mind, though, that you can't transfer SkyMiles to any of SkyTeam's loyalty programs.
Altogether, Delta SkyMiles frequent traveler program is a complicated one and certainly not the most transparent, but it can offer some perks and Delta has gained its loyal fans over time. If you are one of them, then figuring out how SkyMiles work can do a good job towards your mileage balance.