The invention provides anti-complement component antibodies such as anti-C1s antibodies and anti-C1r antibodies, and methods of using the same. The invention also provides pharmaceutical formulations comprising the antibodies, and methods of treating an individual having a complement-mediated disease or disorder comprising administering the antibody to the individual. The binding specificity and C1q displacement function of the anti-C1s antibodies and anti-C1r antibodies are evaluated. Time dependent complement neutralization function and binding to native and truncated C1s or C1r proteins are also shown for the antibodies.