This TOJ has a confession to make: I don't do much old-fashioned static stretching, the kind where you assume a fixed pose and hold it for 30 or more seconds, straining, say, to touch your toes. I prefer dynamic stretching for 95% of my warm-up and cool-down because the benefits are proven by good science and it feels more natural.
I learned to not like static stretching when I played high school football and ran track; it was boring and often hurt. I encountered the old ways again when I studied martial arts after college. That was decades ago, and even then I wondered it it really did any good. Since then exercise physiologists have affirmed static stretching is of limited help in preventing injuries, maybe even harmful, and may reduce your athletic performance rather than enhance it.
A couple years ago, Gretchen Reynolds wrote an article about static and dynamic stretching and the scientific evidence for/against both. Check it out because it's a concise overview of the issues and the superior benefits of dynamic stretching. Also included are some good examples of dynamic stretching. The most important take away point is that static stretching is useful only in small doses.
Dynamic stretching is the best warm up. It's very simple: you gently move the joints of your body prior through their range of motion, especially those parts of your body that will be stressed when you start of exercise hard. Prior to running , it might consist of jogging slowly for a couple of minutes, then gradually running a little faster for a couple more minutes. When preparing to lift weights or do calisthenics and jumps, it might consist of rotating the knees for twenty seconds, rotating the hips for twenty seconds, rotating the upper torso right to left for twenty seconds, then windmilling the arms for twenty seconds. This might be followed by a minute of light jumping with feet shoulder width, hands held loose at the side, and the feet barely leaving the ground, or a few squats and forward knee lunges. You want to just start to sweat and slightly elevate your breathing. That's it.
Unless you are a contortionist in the circus, there's no benefit to being super flexible. The right amount of flexibility enables you to generate some power in your running, lifting, x-c skiing, biking, whatever your sport might be. And some flexibility is absolutely necessary if you take a fall on a bike or slip while running on snow. But flexibility is not an end in itself unless you are a yogi. Strength plays an equal role in protecting you.
Flexibility is largely predetermined by genetics and gender. Women are usually more flexible than men. The body stretches less and less as you grow up because of natural bone growth; for example, you won't be able to do the side splits anymore because your mature femurs are more restricted by the fully developed sockets in your hips.
Dynamic stretching of the joints that will be stressed in your particular activity or sport raises your body temperature, allowing collagen in muscles, tendons, ligaments and joints to become more elastic. With the warmer temperatures comes increased blood supply to all these tissues, which in turn aids in producing metabolic energy and helping muscles quickly contract and relax, thereby generating speed and power.
For TOJs, the warm-up becomes even more important because the circulatory system is not as efficient as we age. The discs in your back, joint surfaces, and tendons have a very limited blood supply. These areas are all especially prone to injury. Dynamic stretching, combined with a light aerobic component, gets the juices (like the synovial fluid lubricating your joints) flowing and your body prepared to exert safely.
Static stretching, in particular classic hatha yoga poses, can help after a workout, especially a hard one. The stretches lengthen and relax the muscles, which in turn allows more oxygen rich blood to flood the tissues to remove the lactic acid, promote more rapid healing of damaged tissues (which occurs in all exercise), and reduce post-workout soreness. (Note that my emphasis here is on preventing athletic injuries. Gentle, controlled static stretching, especially as practiced in yoga, induces relaxation, which is effective for stress reduction.)
A favorite hybrid routine that I use as a warm-up which mixes yoga's Salute to the Sun and some everyday calisthenics like push-ups. Going slowly from movement to movement, I never stop, including during the Downward Facing Dog and Cobra poses, which you'll see people on early morning Yoga TV holding for a minute.
Watch how dogs stretch when they rise after sleeping - it's slow, smooth and continuous. Animals mastered dynamic stretching a long time ago.