Abstract Most of the optimization problems encountered in the real world are discrete type which involves decision variables defined in the discrete search space. Binary optimization problems, integer and mixed integer programming problems are of this category, and they require suitable solution representation and search operators to be solved by nature-inspired algorithms. One of the widely-used and well-known nature-inspired algorithms is Artificial Bee Colony (ABC) that has been originally proposed to solve the problems in the continuous domain, and hence, its standard version employs the search operators to exploit the information of the solution vectors encoded in the continuous domain. To be able to cope with the discrete problems, particularly binary, integer and mixed integer programming problems, which are also a group of numeric optimization problems, various encoding types, search operators and selection operators have been integrated into ABC. In this paper, we review the studies proposing new ABC variants to solve discrete numeric optimization problems. To the best of our knowledge, this will be the first comprehensive survey study on this topic. Therefore, we hope that this study would be beneficial to the readers interested in the use of ABC for the binary, integer and mixed integer discrete optimization problems.