Evolution has been taking place since the first life began, and continues to do so to this day. It is a process by which living organisms change over time that is backed by a large body of scientific evidence and observation.
To give you one example of where it still takes place today, strains of bacteria that are exposed to antibiotics over time will develop a resistance to that same antibiotic. The mutated cells of that bacteria that were originally resistant survive while those that were not died off. The mutated, resistant cells then multiplied, essentially creating a new strain of bacteria the antibiotic has no effect on.
We can also observe the history of evolutionary change by comparing the DNA of one organism to the DNA of a similar one. Humans and Chimpanzees, for example, share much of the same genome, suggesting they were once part of the same species. Mutations and evolution differentiated them over time.
We can also see the process of Natural Selection in humans based on their environment. Descendants of the Incas have larger lung capacities than the average human, because for centuries the tribes have lived in an environment with limited oxygen, and those with larger lung capacities survived at greater rates and multiplied.