This survey paper is a Chapter in the book Problems in Topology. In the paper we defined all small cardinals (i. e, cardinals related to the continuum) known at the time, relations among them and open questions. It contains a status report on all questions in Eric van Douwen's article in the Handbook of Set Theoretic Topology "Functions from the integers to the integers." Also there is an Appendix by S. Shelah with the proof of his theorem

ZFC |-- d \leq i

(that is, the dominating number on functions from the integers to the integers is less than or equal to minimum cardinality of a maximal independent family of subset of the integers).

This on-line version has been updated.