Chromium and arsenic are two of the most problematic water pollutants due to their high toxicity and prevalence in various water streams. While adsorption and ion-exchange processes have been applied for the efficient removal of numerous toxic contaminants, including heavy metals, from water, these technologies display relatively low overall performances and stabilities for the remediation of chromium and arsenic oxyanions. This work presents the use of polyol-functionalized porous aromatic framework (PAF) adsorbent materials that use chelation, ion-exchange, redox activity, and hydrogen-bonding interactions for the highly selective capture of chromium and arsenic from water. The chromium and arsenic binding mechanisms within these materials are probed using an array of characterization techniques, including X-ray absorption and X-ray photoelectron spectroscopies. Adsorption studies reveal that the functionalized porous aromatic frameworks (PAFs) achieve selective, near-instantaneous (reaching equilibrium capacity within 10 s), and high-capacity (2.5 mmol/g) binding performances owing to their targeted chemistries, high porosities, and high functional group loadings. Cycling tests further demonstrate that the top-performing PAF material can be recycled using mild acid and base washes without any measurable performance loss over at least ten adsorption-desorption cycles. Finally, we establish chemical design principles enabling the selective removal of chromium, arsenic, and boron from water. To achieve this, we show that PAFs appended with analogous binding groups exhibit differences in adsorption behavior, revealing the importance of binding group length and chemical identity.