Methods for removing, or leaching, cobalt or other diamond-diamond bonding catalysts from polycrystalline diamond compacts (PDCs) or other structures formed from polycrystalline diamond include leaching under conditions that simulate use of PDCs in a hot hole drilling environment. A leaching agent may be formulated, when used under appropriate conditions, to remove or substantially remove cobalt or another catalyst from polycrystalline diamond without dissolving, degrading or otherwise attacking a substrate that supports or carries the polycrystalline diamond. The leaching agent may include one or more components that mimick the chemicals or conditions to which a PDC would be exposed in a hot hole drilling environment. Polycrystalline diamond structures from which cobalt or another diamond-diamond bonding catalyst has been removed or substantially removed are also disclosed, as are systems for leaching cobalt or other diamond-diamond bonding catalysts from polycrystalline diamond.