While identical twins are similar in almost all aspects, they are also different. From the moment the zygote separates environmental factors start to affect their growth and development. For instance mirror twins are when the twins will have symmetrical features, such as opposite hair whorls or moles on the opposite side of the face. Differences such as placement in the womb and nutrition also play a role. The most notable differences in twins are fingerprints and retina patterns. Neither prints nor retinas are fully genetic. The fingerprints are more similar than even fraternal twins, showing that similar DNA does have an influence, but is not the only deciding factor. The same is true with retinas.
Once twins are born environmental factors immediately affect the twins. Even twins that are raised together are different, and as the grow older the differences become more pronounced. One twin might get sick, while the other will not. Examples such as this are also due genetic differences. While it is true that twins have identical DNA, they may have different copies of a gene. Copy number variants is when a person has more or less than two copies (one from mom and one from dad) of each gene. These differences may account for only one twin getting leukemia. Also, the mitochondrial DNA of each twin may not be exactly the same. The mitochondrial DNA is taken only from the mom, and in identical twins may be slightly different. This would also lead to differences later on in life.
There is also a phenomenon called semi-twins. This occurs when a set of twins has identical DNA from one parent, but different DNA from the other. It is very rare, only a handful of cases have ever been documented. The cause is one egg being fertilized by two sperm, and then splitting into two zygotes which share the same maternal DNA but different paternal DNA.