Convergent evolution is the independent appearance of the same trait in different lineages. Evolutionists assert that such traits are due to homologous DNA sequences that have arisen independently in unrelated organisms by random mutations and similar selective pressures. Futuyma defines convergent evolution as "the independent origin of a derived character state in two or more taxa". In contrasts, creationists and intelligent design theorists attribute such homology to the Creator's repeated use of the same design features in different organisms.
Problems with Evolutionism
Proponents of the theory of evolution have great difficulty explaining how certain highly developed and complex features can reappear among different species even though it there is no explanation for how these features would occur randomly more than a few times throughout natural history. The phenomenon of repeated occurrence of similar design features is compelling evidence that an intelligent Creator does exist. To explain this away, evolutionists claim that "convergent evolution" allows different species to fill the same niche in different ecosystems simply by chance. The theory of convergent evolution is greatly complicated, however, by the fact that many "convergent" traits are developed from different parts of the embryo and therefore are unlikely to have shared a common ancestor. 
Convergent evolution also begins to break down when examined in a specific context. One common issue is with bioluminescence, the design trait of being able to biologically generate light. Bioluminescence requires hundreds of unlikely genetic mutations, yet has emerged more than thirty different times throughout natural history. The chance of this occurring due to evolution of any kind, let alone by random mutation, is widely considered to be very unlikely.
On the other hand, so-called convergence fits well into the Creationist worldview because an intelligent designer would not need "luck" in order to develop a trait repeatedly. In fact, it would be favorable for such a designer to reuse design traits that worked, such as bioluminescence, during the initial scientific event known as Creation week. Those traits that do appear to have occurred due to biological evolution have been shown in more recent studies  to be the result of Genetic recombination, a guided rather than naturalistic process.
|“||An intelligent cause may reuse or redeploy the same module in different systems, without there necessarily being any material or physical connection between those systems. Even more simply, intelligent causes can generate identical patterns independently. ||”|
- Futuyma, Douglas J. (2005). Evolution. Sunderland, Massachusetts: Sinauer Associates, Inc. p. 25. ISBN 978-0-87893-187-3.
- Convergent Genetic Evolution: "Surprising" Under Unguided Evolution, Expected Under Intelligent Design Posted by Casey Luskin on September 1, 2010
- Implications of Genetic Convergent Evolution for Common Descent Posted by Casey Luskin on September 3, 2010
- Life Sciences: Evidence against Convergent evolution
- Sherwin, Frank Living Light Institute for Creation Research. Accessed April 24, 2015.
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- Nelson, P., Wells, J. "Homology in Biology," in Darwinism, Design, and Public Education, pg. 316
- This website aims to tell you nearly everything you need (and may ever want) to know about convergent evolution Map of Life - Convergent Evolution Online.
- Convergence, ID Critics, and Public Theatre Uncommon Descent. April 4, 2011.