The aim of this narrative review was to assess published growth data for healthy, term, infants consuming extensively hydrolyzed protein-based (EHF), or amino acid-based formulas (AAF). These data may be of use to clinicians managing infants with medical conditions consuming these products. A search was conducted using key terms: amino acid-based, hydrolysate, hydrolyzed, hydrolysed, infant formula, infant formulae or formulas, baby formula, or formulae or formulas, infant, infants, infantile, and growth. Seven controlled, randomized, prospective growth trials of healthy term infants fed EHFs or AAFs at similar time points during the first four months of age met these and other criteria, including that the trial was published in a peer-reviewed journal, subjects were enrolled by ≤14 days of age and were exclusively formula-fed at entry and throughout the duration of the trial, and infants were assessed at regular intervals with weight measures available ideally at 14 days, one, two, three, and four months of age. Results suggested that healthy infants receiving commonly available EHFs and AAFs do not appear to experience accelerated growth as reported for infants fed many standard formulas. Differences in growth patterns were observed with some formulas supporting normative growth patterns during the first four months but others appearing to support markedly lower growth patterns. These observations should be confirmed in well-designed prospective randomized trials. Until that time, it is recommended that EHFs and AAFs be chosen carefully with individual patient needs considered.