Many members of the genus are found in dry or open habitats. C. chilensis is common in buttongrass sedgeland and C. purpureocaulis seems to favor rainforest or very wet forest.

While a number of species can be readily identified in the field, cross sectional leaf anatomy is probably the most reliable for species recognition.

The genus was previously placed under the Dicranaceae but recent molecular work has shown that the genus is better accommodated in the Leucobryaceae. Recent taxonomic work with the Australian taxa has also resulted in a number of species name changes.