We report new Hubble Space Telescope WFPC2 and NICMOS observations of the center of the nearest radio galaxy Centaurus A (NGC 5128) and discuss their implications for our understanding of the active nucleus and jet. We detect the active nucleus in the near-IR (K and H) and, for the first time, in the optical (I and V), deriving the spectral energy distribution of the nucleus from the radio to X-rays. The optical and part of the near-IR emission can be explained by the extrapolation of the X-ray power law reddened by AV~14, a value consistent with other independent estimates. The 20 pc scale nuclear disk discovered by Schreier and colleagues is detected in the [Fe II] λ1.64 μm line and presents a morphology similar to that observed in Paα with a [Fe II]/Paα ratio typical of low-ionization Seyfert galaxies and LINERs. NICMOS 3 Paα observations in a 50''x50'' circumnuclear region suggest enhanced star formation (~0.3 Msolar yr-1) at the edges of the putative bar seen with ISO, perhaps due to shocks driven into the gas. The light profile, reconstructed from V, H, and K observations, shows that Centaurus A has a core profile with a resolved break at ~4" and suggests a black hole mass of ~109 Msolar. A linear blue structure aligned with the radio/X-ray jet may indicate a channel of relatively low reddening in which dust has been swept away by the jet.