In online scheduling, jobs are available one by one and each job must be scheduled irrevocably before the availability of the next job. Semi-online scheduling is a relaxed variant of online scheduling, where an additional memory in terms of buffer or an Extra Piece of Information(EPI) is provided along with input data. The EPI may include one or more of the parameter(s) such as size of the largest job, total size of all jobs, arrival sequence of the jobs, optimum makespan value or range of job's processing time. A semi-online scheduling algorithm was first introduced in 1997 by Kellerer et al. They envisioned semi-online scheduling as a practically significant model and obtained improved results for $2$-identical machine setting. This paper surveys scholarly contributions in the design of semi-online scheduling algorithms in parallel machine models such as identical and uniformly related by considering job's processing formats such as preemptive and non-preemptive with the optimality criteria such as Min-Max and Max-Min. The main focus is to present state of the art competitive analysis results of well-known semi-online scheduling algorithms in a chronological overview. The survey first introduces the online and semi-online algorithmic frameworks for the multi-processor scheduling problem with important applications and research motivation, followed by a taxonomy for semi-online scheduling. Fifteen well-known semi-online scheduling algorithms are stated. Important competitive analysis results are presented in a chronological way by highlighting the critical ideas and intuition behind the results. An evolution time-line of semi-online scheduling setups and a classification of the references based on EPI are outlined. Finally, the survey concludes with the exploration of some of the interesting research challenges and open problems.