This work of Dr. Sarfraz Nawaz Malik includes his research which has been acknowledged at different levels. He won the "Research Productivity Award" from his mother institute "COMSATS Institute of Information Technology, Islamabad, Pakistan for four consecutive years (2011-2014). In year 2012, he was declared "Productive Scientist of Pakistan" by Pakistan Council for Science and Technology. The main focus of this study is to develop conic domains and to introduce some new geometrical structures as image domains. The aim is to develop and refine already known conic domains as well as to introduce certain new generalized domains and their associated functions. It also deals with generalized circular domains and introduces certain new classes of analytic functions representing conic and circular domains.