Karma is a law like Newtonian action-reaction.
Jesus said that those who live by the sword shall die by the sword.
Numbers 14:18 tells us that the sins of the fathers shall be visited on the children 3 or 4 generations hence. This passage describes not only karma, but reincarnation, too. For it is only the perpetrator who pays for the sins they commit; not innocent children.
But this effect works only so long as we are attached to ego (self-concern). Ego is a physical cog in the universe -- a pseudo-self to which the spirit has become attached. In fact, ego is pure dichotomy. We see this in the passages of Genesis 3, with the tree of knowledge of good and evil. But ego is more than merely good-evil; it is also right-wrong, generous-selfish, wisdom-stupidity, compassion-indifference, and many more.
If you eliminate self-concern (go neutral on ego), then you are free of karma. But you cannot do this in a vacuum. You need to practice love of others as if they were yourself. When you do this, you help heal the world.