Modern software development relies heavily on frequent updates to dependencies (e.g. third-party libraries, frameworks and APIs), which introduce the need for consistent and efficient migration practices to avoid breaking changes. As these dependencies evolve, developers face the challenge of adapting their code-bases to maintain compatibility, security, and performance. Goal: We investigate the current landscape of dependency version migration, focusing on identifying the motivations, techniques, tools, and challenges to conduct such activity. The study also aims to understand the strategies to detect the need for dependency migration and the trade-offs involved in these decisions. Method: We conducted a rapid review of the literature using the Scopus search engine, which returned 2,637 papers in February 2025. After applying predefined inclusion and exclusion criteria, we ended up with 63 included studies, which we extracted data to answer each of the research questions. Results: The findings indicate that developers rarely migrate dependencies unless strongly motivated by bug fixes, compatibility, or security fixes. The strategies to identify dependencies that require updates rely on automated tools or methods. Typically, strategies to detect breaking changes are manual inspection or the use of specialized tools. Several tools and strategies have been proposed to support dependency updates, many of which rely on static analysis, rule-based transformations, or example-driven techniques. However, these tools often involve trade-offs between precision, usability, and manual effort. Conclusions: This review highlights that dependency migration is not a common practice and when it happens it is for reasons of fixes and compatibility. The proposed strategies to identify dependencies that need to be updated rely on automated tools, on the other hand, the strategies to identify braking changes varies between cases using manual and cases using automation. Furthermore, there is no silver bullet solution in the dependency migration techniques, they have different proposals and specificity.