The main task of engineers is designing and manufacturing of useful products. Rapid progress in science and technology is creating more innovative techniques and more advanced products. For today's engineering graduates to be successful, they must be able to solve complex and open-ended problems, and be capable of independent and critical thinking. Critical thinking (CT) can be simply defined as the analysis of available facts, evidence, observations, and arguments to form a judgment. Nurturing of critical thinking skills in students is generally deemed an uphill task by instructors at engineering universities. Quantitative assessment of CT skills and tasks is an even grayer area. This paper presents an overview of the different issues related to instruction and assessment of CT skills, and the various methods adopted, especially in the context of engineering education. Some of the more interesting issues discussed are classroom exercises for CT assessment; self-assessment of CT skills; CT assessment design, quantification, and summative assessment; taxonomy of CT assessment; and limitations of standardized CT assessment. This brief but in-depth review can be useful for engineering students and instructors targeting the development of CT skills, and for other branches of education. Introduction In a nutshell, engineering is the designing and manufacturing of useful products. Due to rapid advances, products are becoming increasingly innovative and complex [1,2]. Successful engineering graduates should have the ability to solve complex and open-ended problems, and to exercise critical thinking [3-5]. A group of United States companies published a report in 2006 [6] according to which employers rate critical thinking (CT) as the most highly desired skill of recent graduates. However, over 90% of the surveyed employers were of the opinion that college graduates were deficient in CT skills. Though hardly anyone disputes the importance of CT, it is quite evident that CT instruction is inadequately addressed in most college curricula. Even after years of university education, in courses that claim to develop higher-order cognitive thinking, many students graduate with limited CT skills [7].