  This is an expository talk on a topic of classical analysis, arising from the
VMO theory of the topological degree due to Br\'ezis and Nirenberg (1995). We
sketch the history of the subject and some of its recent developments. The
paper is organized as a sequence of questions. Most of them, in particular the
last one, deal with Fourier series of continuous functions of constant absolute
value. One of them contains new results on the comparison of summation
processes.
