The luminous Type IIn SN 2010jl shows strong signs of interaction between the SN ejecta and dense circumstellar material. Dust may be present in the unshocked ejecta; the cool, dense shell (CDS) between the shocks in the interaction region; or in the circumstellar medium (CSM). We present and model new optical and infrared photometry and spectroscopy of SN 2010jl from 82 to 1367 days since explosion. We evaluate the photometric and spectroscopic evolution using the radiative transfer codes MOCASSIN and DAMOCLES, respectively. We propose an interaction scenario and investigate the resulting dust formation scenarios and dust masses. We find that SN 2010jl has been continuously forming dust based on the evolution of its infrared emission and optical spectra. There is evidence for preexisting dust in the CSM as well as new dust formation in the CDS and/or ejecta. We estimate that 0.005-0.01M_{sun}_ of predominantly carbon dust grains has formed in SN 2010jl by ~1400 days post-outburst.