Who is in charge of the Borders?

Is it a national thing that federal government maintains, or a state thing in which federal government must let the states decide.

To me I think it should be a federal border in which the states can act in emergency fashion until the federal government can then come and fix that emergency. Didn't Trump have a hard time in California because the states Jumped in. Could it be that we are now seeing that battle play out in reverse. A way to unify what our border actually is. Is it separate borders based off each state, or is it a federal border in which the states can only act on in emergency. Or is it something else.

I'm not exactly sure what the law says. Can anyone help explain things to me.