How are game animations blended together?

How do games blend together different animations? What I mean by blending is this. Suppose
we are in a fps game and we jump and shoot at the same time. How does both the animations get played together without affecting each other. Another example would be this. In a third person game the character responds with to inputs almost instantly by playing many animations. In one instance the player was moving to the left with full speed and now it is trying to change its direction by slowing himself down and rotating its body. How does something like this is achieved.