Cognitive abilities related to learning ability and intelligence involve 8 levels of fundamental processes. Any and all of such cognitive abilities reduce to these 8 levels or to combinations of them. The 8 levels are hierarchical because lower levels, generally, are prerequisites for higher levels. An animal's general cognitive ability is determined by how many of the fundamental processes it can use. Although the processes are hierarchical, an animal will use all processes available to it in serial or in parallel as the situation requires. A perusal of contemporary journals' contents will show that behavioral neuroscientists, including behavioral pharmacologists, rarely study cognitive abilities that require the use of processes at the highest 4 levels. Yet, all vertebrates may be capable of using level-5 processes, and several avian and mammalian species have been shown to use level-6 processes. The use of level-7 processes has been shown in non-human primates and likely can be shown in non-primate species, too. The present article provides an overview of the basic cognitive processes as well as types of tasks that might be used to investigate the neural correlates or substrates of higher cognitive processes in animals. Unless and until better measures of cognitive ability are used, a vast potential for research will be unrealized.