The Fifth Generation(5G) communication network is envisioned to provide heterogeneous services tailored to specific user demands. These services are diverse and can be generally categorized based on latency, bandwidth, reliability, and connection density requirements. The 5G infrastructure providers are expected to employ network function virtualization, software-defined networking, and network slicing for cost-effective and efficient network resource allocation. In the 5G network, when an infrastructure provider receives a slice request, a slice admission control scheme is applied and an optimization algorithm is used to achieve predefined objectives. To this end, a number of slice admission control objectives, strategies and algorithms have been proposed. However, there is a need to present a coherent review and bridge the gap between many aspects of slice admission control. In this paper, we present the latest developments in this research area. Thus, we begin by introducing slice admission control and discuss background concepts associated with slicing. We then extend our discussion to slice admission objectives followed by the strategies and optimization algorithms. Finally, we conclude with a summary of analysis containing the optimization algorithms.