Here's an excellent video that crams a huge amount of information about life expectancy into less than seven minutes. The speaker is Dr. Aaron Carroll, a pediatrician who also writes extensively about healthcare and related matters (here, and here, for example) and does a series of videos from which this one is taken.
To summarize Dr. Carroll's main points, life expectancy at birth has increased dramatically in the last century, but mainly as a result of vaccines and cures for childhood diseases. Life expectancy at older ages has also gone up, but more modestly. Since 1950, for example, U.S. life expectancy at birth has increased by about 10 years, but life expectancy at 65 is up only half as much. (Even in 1950, people who reached 65 lived to be about 79 on average.)
Moreover, the improvement isn't evenly distributed. For example, over the 30 years from 1977 to 2007, life expectancy at age 65 for people covered by Social Security rose by around five years for those in the top half of the income distribution versus only one year for those in the bottom half.
Even more surprising (as I mentioned in a post back in 2013 here), from 1990 to 2008 life expectancy at age 25 dropped a remarkable five years for white American women who had not finished high school. It dropped by three years for white men without a high school diploma as well. The drop was not seen for black Americans with similar education levels. (This doesn't change the fact that in general, black Americans have substantially lower life expectancy than white Americans, however.)
As Dr. Carroll notes in passing, these facts have implications for Social Security. A surprising number of people who ought to know better get the connections wrong, as mentioned in earlier posts on this blog here and here. The first refers to statements from former Texas Governor (as well as past and likely future presidential candidate) Rick Perry, and not everyone will be surprised that Governor Perry got it wrong. But the second points out a similar misconception of the part of former Senator Alan Simpson (R-Wyoming), co-chairman of the Simpson-Bowles commission on deficit reduction.
A final note on life expectancy that I've mentioned before but merits repeating: Life expectancy is a statistical concept that differs from the more general notion of a "normal lifespan," meaning how long people can expect to live if they don't die young from accident, disease, or violence. Unlike life expectancy, the normal human lifespan has changed only a little over the course of history. Even the 90th Psalm, written 25 or 30 centuries ago, says, "The days of our years are threescore years and ten; and if by reason of strength they be fourscore years, yet is their strength labour and sorrow; for it is soon cut off, and we fly away." (Psalm 90:10 KJV). We're not talking here about the vast legendary lifespans in Genesis; the Psalmist was addressing the adults of his own day who viewed 70 or 80 as a typical lifespan.
(Updated 2018 March 21 to clarify some wording in the last paragraph.)