This expository talk will try to bridge the first examples of "almost commuting" unitary matrices that are not almost "commuting unitaries" due to Voiculescu to a more sophisticated and very beautiful construction of examples by Gromov and Lawson in the early 80's that is intimately connected to deep phenomena in topology and geometry related to the role of fundamental group. It can serve as an introduction to Dadarlat's talk. If I inadvertently say anything new and correct, it will be joint work with Alex Lubotzky or Guoliang Yu. However, I expect that most of the talk will be about ideas well known before half the audience was born.