The Monniot collection of copepods associated with ascidian hosts was built up over several decades of field collecting and taxonomic research on ascidians by Drs Claude Françoise Monniot (MNHN, Paris). This paper describes a total of 84 new species of copepods collected from ascidian hosts and five new genera are established. Prior to this study the family Ascidicolidae comprised two genera accommodating five valid species; here we add two new genera, Hamistyelicola gen. nov. and Bathycopola gen. nov., and eight new species in total. The family Buproridae comprised a single genus consisting of three species; here we add a new monotypic genus, Buprorides gen. nov. The family Botryllophilidae comprised 68 valid species in seven genera and here we add 45 new species; 13 of Botryllophilus Hesse, 1864, nine of Schizoproctus Aurivillius, 1885, three of Haplostomides Chatton Harant, 1924, 12 of Haplostoma Chatton Harant, 1924, seven of Haplostomella Chatton Harant, 1924 and a single new species of Haplosaccus Chatton Harant, 1924. The Enteropsidae comprised 42 species in five genera and here we add two new genera, Monnioticopa gen. nov. and Periboia gen. nov., plus a total of 30 new species; 15 of Enterocola van Beneden, 1860, two of Enterocolides Chatton Harant, 1922, five of Enteropsis C.W.S. Aurivillius, 1885, five of Monnioticopa gen. nov., two of Mychophilus Hesse, 1865, plus the type species of Periboia gen. nov. Generic diagnoses are provided for all genera represented in the collection. A further 13 known species are also reported and brief supplementary descriptive notes or full redescriptions are provided, as appropriate.