Whilst Ehrenberg only knew the skeleton of the Polycystina solitaria, the first observations of living Cyrtida were published by Johannes Müller, 1858, in his fundamental treatise. He gave the first description and figures of the central capsule of this group, with the characteristic lobes developed from its basal part; and of the pseudopodia radiating on all sides (_loc. cit._, Taf. vi.). The forms described by him were all Mediterranean, one Dicyrtid (_Lithomelissa mediterranea_), two Tricyrtids (_Eucyrtidium zancleum_ and _Pterocanium charybdeum_), and one Stichocyrtid (_Lithocampe tropeziana_). In my monograph (1862, p. 272-341) I gave a detailed description of all known and some new Cyrtida, and characterised this family by the fundamental monaxonial form of the shell, with two different poles (an upper apical and a lower basal pole), and by the unipolar growth, beginning from the apical pole. I pointed out also the peculiar structure of the monaxonial central capsule. At that time I divided the Cyrtida into five subfamilies, in which, however, the #Spyroidea# (= Zygocyrtida), and the #Botryodea# (= Polycyrtida) were united with the true #Cyrtoidea# (Monocyrtida, Dicyrtida, Stichocyrtida). The astonishing number of new and interesting forms of Cyrtida which I found in the rich collection of the Challenger (beginning from 1876), and mainly in the Radiolarian ooze of the Central Pacific (Stations 263 to 274), enabled me to give in my Prodromus, in 1881, a greatly enlarged and amended system of this important group. I separated there the #Spyroidea# (= Zygocyrtida), and the _Botryodea_ (= Polycyrtida) from the true #Cyrtoidea# by restricted definition, pointing out the essential differences in the structure of the cephalis in these groups of #Cyrtellaria#. The latter name, as here used, is therefore identical with the "Cyrtida" of my Monograph. In the Prodromus I divided the true Cyrtida (p. 426) into five subfamilies and thirty tribes, corresponding to the differences in the number of the shell-joints and of the radial apophyses, and in the shape of the closed or open mouth. These groups are here retained, but reduced to four families and twenty-four subfamilies, since the Tetracyrtida are better united with the Stichocyrtida (compare below). Richard Hertwig in his work Organismus der Radiolarien (1879, pp. 74 to 86) gave the first accurate description of the finer structure of the central capsule of the Cyrtida, and pointed out their character as true MONOPYLEA, with porochora and {1128}podoconus, and the peculiar shape of its nucleus. He also published excellent figures of some interesting new species.