The influence maximization (IM) problem identifies the subset of influential users in the network to provide solutions for real-world problems like outbreak detection, viral marketing, etc. Therefore, IM is an essential problem to tackle some real-life problems and activities. Accordingly, many reviews and surveys are presented, and most of them mainly focused on classical IM frameworks for single networks and avoided other IM frameworks. In this context, the IM problem still has some important design aspects along with some new challenges of the problem. Inspired by these facts, a comparative survey of the state-of-art approaches for IM algorithms is presented in this paper. To build the foundation of IM problem, firstly, the well-accepted information diffusion models are discussed. Secondly, a comprehensive study of IM algorithms along with a comparative review is presented based on algorithmic frameworks of IM algorithms. A relative analysis of IM approaches regarding performance metrics is discussed next. At last, the upcoming challenges and future prospects of the research in this field are discussed.