Where do LDLs and HDLs carry cholesterol to and from??

HDL acts as a scavenger, carrying LDL (bad) cholesterol away from the arteries and back to the liver, where the LDL is broken down and passed from the body. But HDL cholesterol does not completely eliminate LDL cholesterol.

Ok so, is this what happens:
- LDL carries cholesterol to cells
- too much LDL cholesterol can cause a build up of cholesterol in artery walls
- HDL cholesterol carries cholesterol from artery walls to liver where it can be removed from body ??