Symmetric and asymmetric cryptographic algorithms are used for a secure transmission of data over an unsecured public channel. In order to use these algorithms in real-time applications, many flexible hardware architectures have been proposed and implemented with multiple design constraints. Therefore, a systematic study is required to analyze various implementation approaches. This paper has focused on the identification and classification of recent research practices pertaining to the flexible hardware implementation of cryptographic algorithms. We have used Systematic Literature Review (SLR) process to identify 51 research articles, published during 2008–2017. The identified researches have been classified according to three design approaches: (1) crypto processor, (2) crypto coprocessor and (3) multicore crypto processor. Consequently, a comparative analysis of various cryptographic algorithms in terms of flexibility, throughput, area, power and implementation technology has been presented. A comprehensive investigation of flexible architectures for implementing cryptographic algorithms facilitates researchers and designers of the domain to select an appropriate design approach for a particular algorithm and/or application according to their needs.