The evolution of the modern silkworm can be traced through its full taxonomy classification: Animilia Arthropoda Insecta Macrolepidoptera Bombicidae Mori. As the larvae of moths, silkworms fall under the Order Lepidoptera, the same as butterflies as well as moths. The fossil record for Lepidoptera is lacking due to their soft-bodies and lack of hard exo-skeleton. There are a few fossils though, and these allow us to track the history of the Lepidoptera as far back as the Triassic when they diverged, along with Trichoptera from a common ancestor. The superfamily Apoditrysia contains all of the large modern moths and butterflies, including the silkworm, and split off during the early 
hylogenetic_chart_of_Lepidoptera.svg">Cretaceous.
In more recent times, the silkworm was bred from its wild state, Bombyx Mandarina, to its domestic one, Bombyx Mori. Over the past 5000 years the domestication process split Mori off of the Chinese Silkworm, rather than the Japanese Silkworm, which diverged approximately 23,600 years ago.
There are a variety of modern silkworm variants. By far the most common silkworm is the Bombyx Mori, which is raised in China and India and provides the majority of silk in the form of mulberry silk. The silkworm Antheraea mylitta produces Tasar silk, which is not as smooth as mulberry silk, and is used as a less fine cloth for interiors and furnishing. Oak Tasar is a subtype of this silk produced by Antheraea pernyi, and is a finer type of Tasar. By far the most major difference between wild and domesticated silkworms is that the adult Bombyx have lost the ability to fly.
There is some evidence of horizontal gene transfer (HGT) playing a role in silkworm evolution. Horizontal gene transfer is any asexual process which results in the transfer of genes from one organism to another. In silkworms the plausible mechanisms for HGT are transformation and transposable elements. Transformation is the absorption of gene fragments by a cell from its environment, while transposable elements are pieces of genetic material that can be passed between organisms, sometime transferring antibiotic resistance. HGT is one of the ways in which organisms evolve over time, and in silkworms it may have resulted in disease resistance. These gene transfers are a legacy from the ancestors of modern domesticated silkworms, and are primarily from bacteria. The research into what these gene fragments do in silkworms is ongoing and mainly focuses on finding new pesticides and how insects adapt to them.