The adjective cognitive especially in conjunction with the word computing seems to be a trendy buzzword in the artificial intelligence community and beyond nowadays. However, the term is often used without explicit definition. Therefore we start with a brief review of the notion and define what we mean by cognitive reasoning. It shall refer to modeling the human ability to draw meaningful conclusions despite incomplete and inconsistent knowledge involving among others the representation of knowledge where all processes from the acquisition and update of knowledge to the derivation of conclusions must be implementable and executable on appropriate hardware. We briefly introduce relevant approaches and methods from cognitive modeling, commonsense reasoning, and subsymbolic approaches. Furthermore, challenges and important research questions are stated, e.g., developing a computational model that can compete with a (human) reasoner on problems that require common sense.