It is argued in this paper that demands for critical thinking (CT) will be determined by needs both of political superstructure and productive forces of a competitive society in the 21st century. Phenomenon of CT has to be studied and understood as one of the essential elements of some more complex entities – higher-order thinking, core of work-related skills, etc. CT skill need to be developed in connection with relevant cognitive and affective dispositions. It is pointed out, therefore, that it is more correct not to be limited by teaching CT but to educate a critical thinker, whose CT skill is relied on base of relevant dispositions. The process of educating a critical thinker, or rather – a person who will have CT, for instance, as element of a set of the core work-related skills, should continue during the kindergarten, school and university education at least. It is substantiated that under conditions of Ukrainian higher education it is expediently to use two interconnected courses in the process of CT education: logic with elements of critical thinking – in frame of the bachelor’s degree studies – and critical thinking on base of logic – in frame of the master’s degree studies.