Scheduling projects are very important topic in project management science. Constrained resources project scheduling problem CRPSP is a problem of the purpose of allocating the available resources to specific tasks or activities for achieving specific objectives or purposes such as minimising the makespan or time of the projects, minimising the execution cost of the project, or any other specific objective or more than one objective at the same time (multi-objectives resource constrained project scheduling problems). This paper introduces a survey for procedure scenarios, techniques, and models that are considered the main context history of CRPSP and multi-mode constrained resource project scheduling problems MMCRPSP. It aims to exhibits, highlights, and update the recent CRPSP surveys. The current state of art for recent researches is evaluated and the potential research directions and orientations are pointed. Also a new framework is proposed for the researchers of interest for this domain of research.