Here we discuss the role of Computational Thinking (CT), Engineering Education Epistemology (EEE) , Computational Science Education (CSE) and the integration of Arts with STEM in education and more generally in learning and teaching approaches and learning objectives. We present arguments from research articles and we propose activities that support our model for Computational STEAM Pedagogy. The purpose of the literature review is to outline research studies in the different forms of STEAM integration and to highlight how CT, EEE, CSE and Arts can be used in this integration and what epistemology can support this holistic approach . The main objective is to summarise what is currently known about the STEAM approaches and to add to the existing literature with a primary model which connects EEE with the Computational pedagogical knowledge mode. The bibliography presents materials covering theoretical considerations around Computational Thinking, Engineering Epistemology, STEM Epistemology, Computational Science in Education and Arts in STEAM. Literature review was conducted using several web-based search engine tools like Web of Science, Google Scholar and open Google searches.