My experience is in cancer research. Our lab does patient derived xenografts (PDX) - basically, we grow the patients' tumors in immunodeficient mice. We can passage the tumor onto subsequent generations of mice as the first animal's tumor burden becomes too large.

Other methods include knockout mice and rats where specific genes are knocked out in an animal (such as TP53, a tumor suppressor gene). Some of the offspring of the animals will also inherit the knocked out gene.