Immortality will unlikely mean we simply live longer and get older. Long, or ultimately immortal, life is likely to be qualitatively different from life as we know it today. Probably, life will initially prolonged through bionically enhanced body replacement parts. Over time, replacement parts could become enhanced parts that increasingly differ from Andy improve on the organic originals they replace. As our mind controls non-organic/artificial/enhanced body parts, the original organic body is discarded. In the end, there may just be a part of the brain that contains our consciousness that directs a web of computers around us. Our consciousness could live in a virtual reality world in eternal happiness. Immortality may come in an entirely different form of course.
But immortality will come. We are too close to it already with artificial limbs that can be directed by our mind. The biggest steps to immortality seem already behind us. Humans will invest more and more as those investments yield concrete enhancements and prolongation of individual lives. The incentives are just too strong.
One interesting side effect of immortality could be the end of religion. Many religions are based on the desire for immortality. Some promise eternal life in heaven or threaten eternal life in hell. Others promise eternal reincarnation. If immortality is put into the real of human achievements, religion will loose its power and appeal. The world could be saved the enormous sufferings and the wars triggered by religious zeal and hatred.