Luminous X-ray emission is considered a universal property of active galactic nuclei (AGNs), and built upon this idea are extragalactic X-ray surveys for finding AGNs efficiently throughout the universe. I will introduce two types of exceptional X-ray weak type 1 quasars in this talk: intrinsically X-ray weak broad absorption line (BAL) quasars and weak emission-line quasars (WLQs). Via NuSTAR hard X-ray observations of a small sample of BAL quasars with <10 keV weakness, we suggested that the X-ray weakness is intrinsic in at least some of the targets. We conducted an X-ray and multiwavelength study of 51 WLQs, and found that about half of these quasars are X-ray weak that is likely due to intrinsic absorption. Implications of these results for the quasar accretion disks, broad emission-line regions, and disk winds are discussed.