A method for treating wastewater that contains biologically refractory and/or bio-inhibitory compounds, the method comprising: mixing wastewater containing biologically refractory and/or bio-inhibitory compounds with a granular activated carbon adsorbent material in a high flux mixing zone (360/370; 460/470; 560/470; 659) for a time sufficient for adsorption of the biologically refractory and/or bio-inhibitory compounds from the wastewater onto the adsorbent material; wherein at least 99.5 wt% of the adsorbent material has an effective granular size above a bottom limit of about 0.3 millimeters, wherein the adsorbent material is porous and is characterized by adsorptive capacity for adsorption of biologically refractory compounds and biologically inhibitory compounds, and capacity for micro-organisms adhered to the adsorbent material, wherein the combined adsorbent material characteristics contribute to biological regeneration of the adsorbent material separating and removing a major portion of the wastewater (371; 471; 571; 671) from the mixture of wastewater and adsorbent material having biologically refractory and/or bio-inhibitory compounds adsorbed thereon; passing the adsorbent material having biologically refractory and/or bio-inhibitory compounds adsorbed thereon and a minor portion of the wastewater (372; 472; 572; 672) to a low flux biological regeneration reactor (302; 402; 502; 602); retaining the adsorbent material and wastewater in suspension in the biological regeneration reactor for a period of time that is sufficient to allow microorganisms in the biological regeneration reactor to biologically act on at least a portion of the adsorbed biologically refractory and/or bio-inhibitory compounds; discharging biologically treated water effluent (308; 408; 508; 608) from the biological regeneration reactor; removing solids from biological regeneration reactor water effluent with a solids separation apparatus (304; 404; 595; 604); passing the biological regeneration reactor water effluent (308; 408; 508; 608) through a separation subsystem (322; 422; 522; 622) in the biological regeneration reactor or downstream of the biological regeneration reactor and between the biological regeneration reactor and the solids separation apparatus to introduce the biological regeneration reactor water effluent, substantially free of adsorbent material, to the solids separation apparatus; and recycling regenerated adsorbent material to the mixing zone (360; 460; 560; 659). mixing wastewater containing biologically refractory and/or bio-inhibitory compounds with a granular activated carbon adsorbent material in a high flux mixing zone (360/370; 460/470; 560/470; 659) for a time sufficient for adsorption of the biologically refractory and/or bio-inhibitory compounds from the wastewater onto the adsorbent material; wherein at least 99.5 wt% of the adsorbent material has an effective granular size above a bottom limit of about 0.3 millimeters, wherein the adsorbent material is porous and is characterized by adsorptive capacity for adsorption of biologically refractory compounds and biologically inhibitory compounds, and capacity for micro-organisms adhered to the adsorbent material, wherein the combined adsorbent material characteristics contribute to biological regeneration of the adsorbent material separating and removing a major portion of the wastewater (371; 471; 571; 671) from the mixture of wastewater and adsorbent material having biologically refractory and/or bio-inhibitory compounds adsorbed thereon; passing the adsorbent material having biologically refractory and/or bio-inhibitory compounds adsorbed thereon and a minor portion of the wastewater (372; 472; 572; 672) to a low flux biological regeneration reactor (302; 402; 502; 602); retaining the adsorbent material and wastewater in suspension in the biological regeneration reactor for a period of time that is sufficient to allow microorganisms in the biological regeneration reactor to biologically act on at least a portion of the adsorbed biologically refractory and/or bio-inhibitory compounds; discharging biologically treated water effluent (308; 408; 508; 608) from the biological regeneration reactor; removing solids from biological regeneration reactor water effluent with a solids separation apparatus (304; 404; 595; 604); passing the biological regeneration reactor water effluent (308; 408; 508; 608) through a separation subsystem (322; 422; 522; 622) in the biological regeneration reactor or downstream of the biological regeneration reactor and between the biological regeneration reactor and the solids separation apparatus to introduce the biological regeneration reactor water effluent, substantially free of adsorbent material, to the solids separation apparatus; and recycling regenerated adsorbent material to the mixing zone (360; 460; 560; 659).