Siskins belong to the genus Carduelis in the finch family. This is a large genus that includes goldfinches, linnets, and siskins. Here I include only the siskins. They can be divided into the Northern Siskins and Neotropical Siskins.
Northern siskins
Eurasian Siskin, or Spruce Siskin, Carduelis spinus
Pine Siskin, Carduelis pinus
Black-capped Siskin, Carduelis atriceps
Antillean Siskin, Carduelis dominicensis
Neotropical siskins
Andean Siskin, Carduelis spinescens
Black Siskin, Carduelis atrata
Black-chinned Siskin, Carduelis barbata
Black-headed Siskin, Carduelis notata
 Black-Hooded Siskin, Carduelis magellanica
 Santa Cruz Siskin, Carduelis (magellanica) santaecrucis
Olivaceous Siskin, Carduelis olivacea
Red Siskin, Carduelis cucullata
Saffron Siskin, Carduelis siemiradzkii
Thick-billed Siskin, Carduelis crassirostris
Yellow-bellied Siskin, Carduelis xanthogastra
Yellow-faced Siskin, Carduelis yarrellii
Yellow-rumped Siskin, Carduelis uropygialis

Photos are available for the species highlighted in red.