When I went to Kazakhstan, lab travel did the arrangements and royally screwed me on frequent flier miles by putting me on three different carries who don't share miles. This trip, I did my own itinerary and took Delta for the entire thing (except for the Moscow -> Vienna flight, which they don't offer). As a result, I netted just over 19,000 frequent flier miles from the flights on this trip. This brings my current Delta total to 27,626. Also, my five nights at the Marriott Grand in Moscow will also give me additional miles, but they won't be credited for some time.
The theshold for their lowest perks club membership is 25,000 miles ("Silver Medallion Member"), which I gather I should now have... though my online statement still says I'm in the base membership class. Maybe that upgrade takes time too, dunno...
Never having been a frequent flier before, I didn't really understand what good miles were other than trading in for discounts on tickets. I can certainly spend my miles on free tickets; I already have enough miles for a free round-trip ticket anywhere in the US. Another flight to Russia or Kazakhstan and I'll have enough for a round-trip ticket to Europe. However, the benefits of having frequent flier status on the airline really comes into play for free upgrades on my routine business travel.
Mike's been flying across the Atlantic several times a year for the last few years, and now he's "Platinum" status, so he basically gets upgraded to business class every time. While I was sitting at the back of the plane, smelling the bathroom and listening to the screaming kids, he was in the first row being served free drinks and enjoying the ability of his plush chair to fully recline. He didn't even request the upgrade; they just automagically do it for any available business class seats, starting with the people in economy who have the most miles and working down until they run out of nice seats. And the best part is that it doesn't cost him miles to get the upgrade.
Also, once you are in the higher eschelons of frequent flier status, the rewards are exponential. He gets double miles for every flight he takes just for being Platinum, so it's even easier for him to acrue miles for free flights. I figure by the time I'm no longer a postdoc, I should at least be Gold status and hopefully won't always be in the worst seat on the plane.
FF benefits also include separate check-in lines at the airport, (sometimes) separate lines to go through security, and you get access to more seats on the plane when you book (you can book exit rows, etc.). Also, re: your specific status, the miles generally need to be accrued during one calendar year and must be "qualifying" miles. Miles accrued through staying at hotels, by credit card purchases, and bonus miles for buying tickets online (or some other kind of speacial deal) generally aren't qualifying, and some miles on partner airlines don't qualify either. Only those miles flown usually count.