The multiplicity problem will be reviewed in some areas of scientific research, where it raises special difficulties. I shall give examples of the way by which the problem is being handled currently - mostly by ignoring it. Dificulties with traditional FWE controlling procedures which might cause this response will be discussed. Recent developments within the FDR control approach will be presented, making this approach especially atractive for these scientific areas. In some cases FWE control is crucial - so I shall discuss how to combine FDR control and FWE control for that purpose.