Computational simulations which include three-dimensional (3-D) image processing and biomechanical calculations should provide useful information to our research and orthodontic clinic as a clinical tool defined as 'thinking'. In this review, 1) biomechanical simulations applied to predict the mandibular growth; 2) mathematical models of virtual bone cells and 3) 3-D images and solid model simulations for surgical planning are introduced. In biomechanical simulation, biting force, electromyographic (EMG) activity and cephalograms of 32 subjects were applied. Computational results of mathematical model were compared with actual bone growth in a rat. Three-dimensional image and solid model of 14 patients were utilized for their treatment planning. From the results, several concepts of our simulations were confirmed: 1) reaction forces generated by masticatory muscles at the condyle control the direction of mandibular growth; 2) some mathematical models have the possibility to describe the process of bone growth; 3) 3-D image processing software and solid models are necessary for diagnosis and planning of orthognathic surgery. We also believe that the orthodontists can more accurately predict the affects of surgical procedures and orthodontic tooth movement using the new cone beam X-ray computed tomography (CT) (CB MercuRay; Hitachi Medico Technology, Tokyo, Japan) and its advanced application software.