  This entry introduces the main features of constructive and intuitionistic set theories. As the field is expanding at a fast  pace, we can only briefly recall some key aspects of results and available techniques. We focus more on constructive set theory to highlight important foundational issues that arise within it. Note that we omit a conspicuous part of the literature  on constructive and intuitionistic ZF which relates to their categorical  interpretations. This area has seen major developments over the years, so much  so that an adequate treatment of that progress would require a  substantial extension of this entry.  The interested reader might wish to consult the entry on   category theory   and its references (see also its  supplement Programmatic Reading Guide). 