Terephthalic acid (PTA), a monomer in the synthesis of polyethylene terephthalate (PET), is obtained by the oxidation of petroleum-derived p-xylene. There is significant interest in the synthesis of renewable, biomass-derived PTA. Here, routes to PTA starting from oxidized products of 5-hydroxymethylfurfural (HMF) that can be produced from biomass are reported. These routes involve Diels-Alder reactions with ethylene and avoid the hydrogenation of HMF to 2,5-dimethylfuran. Oxidized derivatives of HMF are reacted with ethylene over solid Lewis acid catalysts that do not contain strong Brønsted acids to synthesize intermediates of PTA and its equally important diester, dimethyl terephthalate (DMT). The partially oxidized HMF, 5-(hydroxymethyl)furoic acid (HMFA), is reacted with high pressure ethylene over a pure-silica molecular sieve containing framework tin (Sn-Beta) to produce the Diels-Alder dehydration product, 4-(hydroxymethyl)benzoic acid (HMBA), with 31% selectivity at 61% HMFA conversion after 6 h at 190 °C. If HMFA is protected with methanol to form methyl 5-(methoxymethyl)furan-2-carboxylate (MMFC), MMFC can react with ethylene in the presence of Sn-Beta for 2 h to produce methyl 4-(methoxymethyl)benzenecarboxylate (MMBC) with 46% selectivity at 28% MMFC conversion or in the presence of a pure-silica molecular sieve containing framework zirconium (Zr-Beta) for 6 h to produce MMBC with 81% selectivity at 26% MMFC conversion. HMBA and MMBC can then be oxidized to produce PTA and DMT, respectively. When Lewis acid containing mesoporous silica (MCM-41) and amorphous silica, or Brønsted acid containing zeolites (Al-Beta), are used as catalysts, a significant decrease in selectivity/yield of the Diels-Alder dehydration product is observed.