What are the limitations of these tests?

One major drawback of antibody tests is the "window" period: the time it takes the body to produce antibodies after infection has begun. The standard tests for HIV do not detect the virus itself, but the antibodies that the body produces in response of the infection. During the period before the antibodies are produced, a person can be infected with HIV and can infect others, but still test negative on the HIV antibody test.