The failure of engineering education in Nigeria has been blamed on many factors from various research findings. To have an in-depth view of some of the problems, this study reviewed research findings on the methods of teaching engineering and related programs in Nigerians institutions of learning. The study reviewed articles and theses on teaching methods in Nigeria, skills need of the 21st century and the 4th industrial revolution, and how the existing teaching methods impart the needed skills. The review showed that: the most popular teaching methods of teaching engineering and related programs in Nigeria are lecture method, laboratory experiment, field trip and final year practical project; the skills that the 21st century industry and 4IR demand are critical thinking, innovation and creativity, problem solving, teamwork, life-long learning, and communication skills; the teaching methods employed in Nigeria are not able to impart the needed skills. The researchers, therefore recommended innovative, students centered learning like problem based learning, project based learning, inquiry based learning and well as effective utilization of instructional resources like multimedia, simulations and virtual laboratory for the teaching and learning of engineering, science and technology programs