This depends on your definition of what it means to be alive. Viruses do possess certain characteristics that are associated with living organisms but lack others which are often thought to be the defining properties of life.
They are made up of organic material such as nucleic acids (DNA or RNA), proteins, lipids and carbohydrates, however, they do not have a cellular structure and therefore cannot metabolise, grow and divide as living cells would do.
Viruses can replicate within a host cell and therefore are able to evolve through the accumulation of mutations in their DNA (or RNA) and the process of natural selection. However, as viruses are entirely dependent on the host organism and therefore cannot survive by themselves, the generally accepted view is that viruses are not alive. They can be thought of more as organic machines which are able to replicate only by hijacking the cellular machinery of the host organism.