Stochastic computing (SC) is an error-tolerant computing technique where computation takes place on randomized statistical bit streams. The main feature is that standard digital logic gates with low power and low area can be used to implement complex arithmetic functions. However, these advantages need to be compared against slow speed and less precision. Also, the area required by stochastic number generators (SNGs) is high as compared with the area required to implement computation circuit. So, if multiple SNGs are used, then the advantage of low area cannot be extracted. So, there is a need to design good quality, reliable and higher throughput SNGs. Out of different approaches that are used to design SNG, use of low discrepancy sequences and randomization functions has better results with respect to throughput and correlation management, respectively, at the cost of area. So, more research using these two approaches can lead to design of efficient SNG. This paper reviews the background, fundamental concepts, basic arithmetic operations using SC, various approaches to design efficient SNG’s by managing correlation in stochastic computing circuits, advantages, and drawbacks followed by conclusion and future challenges. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.