The DKIST wavefront correction system will be an integral part of the telescope, providing active alignment control, wavefront correction, and jitter compensation to all DKIST instruments. The wavefront correction system will operate in four observing modes, diffraction-limited, seeing-limited on-disk, seeing-limited coronal, and limb occulting with image stabilization. Wavefront correction for DKIST includes two major components: active optics to correct low-order wavefront and alignment errors, and adaptive optics to correct wavefront errors and high-frequency jitter caused by atmospheric turbulence. The adaptive optics system is built around a fast tip-tilt mirror and a 1600 actuator deformable mirror, both of which are controlled by an FPGA-based real-time system running at 2 kHz. It is designed to achieve on-axis Strehl of 0.3 at 500 nm in median seeing (r0 = 7 cm) and Strehl of 0.6 at 630 nm in excellent seeing (r0 = 20 cm). We present the current status of the DKIST high-order adaptive optics, focusing on system design, hardware procurements, and error budget management.