We are no closer to attaining immortality of the body at all. We can cure and/or treat certain diseases and conditions of the body which undoubtedly extends our lives past the malady. However, certain things cannot be overcome. Most deaths are not caused by old age but by other means, however, when all else fails old age catches up and will always catch up.
There is only one living creature that I am aware of that is thought to be immortal and that is the flatworm. It regenerates itself continuously and never seems to die.
We, however, are not flatworms.