Living with Infinities

This is the written version of a talk given in memory of Gunnar K"{a}ll'{e}n, at the Departments of Theoretical Physics, Physics, and Astronomy of Lund University on February 13, 2009. It will be published in a collection of the papers of Gunnar K"{a}ll'{e}n, edited by C. Jarlskog and A. C. T. Wu. I discuss some of K"{a}ll'{e}n’s work, especially regarding the problem of infinities in quantum field theory, and recount my own interactions with him. In addition, I describe for non-specialists the current status of the problem, and present my personal view on how it may be resolved in the future.