A good review article by Lloyd N. Trefethen is here. It's slated to appear in the Princeton Companion to Mathematics. You can find numerous other preprints of chapters that are forthcoming just by googling the title. In any case, the Trefethen article is well worth checking out for anyone interested in what NA is all about these days.
Also on Trefethen's site are a number of other good reads:
- The definition of numerical analysis
- Maxims about numerical mathematics, computers, science, and life
- Predictions for scientific computing 50 years from now
- Numerical Software Tools and Information Sources
- Classic papers of numerical analysis (and most of the papers themselves)