I'm almost 61 and I don't consider myself old. I am in great shape, strong, weigh the same as I did at 25. I do need more stretching and recovery, and speed is not as important to me.
I've dealt with the 2 issues Laurelmore mentions, but, I keep going.
I am younger than most of the people in my riding group, who do little things like run the Boston Marathon, ride 200 miles a week, Gran Fondos, gravel grinders, on and on and on. I'm a slouch compared to some of them.