Thermally stable polycrystalline constructions comprise a diamond body joined with a substrate, and may have a nonplanar interface. The construction may include an interlayer interposed between the diamond body and substrate. The diamond body preferably has a thickness greater than about 1.5 mm, and comprises a matrix phase of bonded together diamond crystals and interstitial regions disposed therebetween that are substantially free of a catalyst material used to sinter the diamond body. A replacement material is disposed within the interstitial regions. A population of the interstitial regions may include non-solvent catalyst material and/or an infiltrant aid disposed therein. The diamond body comprises two regions; namely, a first region comprising diamond grains that may be sized smaller than diamond grains in a second region, and/or the first region may comprise a diamond volume that is greater than that in the second region.