The extension of a given instruction-set with specialized instructions has become a common technique used to speed up the execution of applications. By identifying computationally intensive portions of an application to be partitioned in segments of code to execute in software and segments of code to execute in hardware, the execution of an application can be considerably speeded up. Each segment of code implemented in hardware can then be seen as a specialized application-specific instruction extending a given instruction-set. Although a number of approaches exist in literature proposing different methodologies to customize an instruction-set, the description of the problem consists only of sporadic comparisons limited to isolated problems. This survey presents a unique detailed description of the problem and provides an exhaustive overview of the research in the past years in instruction-set extension. This article presents a thorough analysis of the issues involved during the customization of an instruction-set by means of a set of specialized application-specific instructions. The investigation of the problem covers both instruction generation and instruction selection and different kinds of customizations are analyzed in a great detail.