Outsourcing confidential data to cloud storage leads to privacy challenges that can be reduced using encryption. However, with encryption in place, the utilization of the data is reduced, which leads to reduced quality of experience of the users. To overcome this, searchable encryption (SE) schemes are utilized, which allow the end users to retrieve the relevant documents from the cloud, for which various researchers have worked utilizing different techniques. Despite the popularity of the searchable encryption schemes, most of the surveys either do not provide or present an incomplete taxonomy of SE schemes. Hence, in this paper, we attempt to present a complete taxonomy/classification of the searchable encryption schemes in terms of the type of search, type of index, results retrieved, implementation type, multiplicity of users, and the technique used. From the literature, it is observed that inner product similarity is widely adopted by researchers to compute the similarity of the query and the document index as it provides both conjunctive and disjunctive searching (ie, have better search capability) but requires high search time (ie, have lower search efficiency). On the other hand, schemes based on binary comparisons exist, which require less search time (ie, have better search efficiency) but support only conjunctive searching (ie, have limited search capability). Thus, a major conclusion drawn from our work is that there is an imbalance between search capability and search efficiency, ie, in the existing schemes, search capability can be improved at the cost of search time only. Therefore, we suggest that one direction where researchers should work on is to provide a balance between search capability and search efficiency.