We present HST UV/optical imaging, Spitzer mid-IR photometry, and optical spectroscopy of a sample of 30 low-redshift (z=0.1-0.3) galaxies chosen from SDSS/GALEX to be accurate local analogs of the high-z Lyman Break Galaxies. The Lyman Break Analogs (LBAs) are similar in mass, metallicity, dust, SFR, size and gas velocity dispersion, thus enabling a detailed investigation of processes that are important at high-z. The optical emission line properties of LBAs are also similar to those of LBGs, indicating comparable conditions in their ISM. In the UV, LBAs are characterized by complexes of massive star-forming clumps, while in the optical they most often show evidence for (post-)mergers/interactions. In 6 cases, we find an extremely massive (>10^9 Msun) compact (R~100 pc) dominant central object (DCO). The DCOs are preferentially found in LBAs with the highest mid-IR luminosities and correspondingly high SFRs (15-100 Msun/yr). We show that the massive SF clumps (including the DCOs) have masses much larger than the nuclear super star clusters seen in normal late type galaxies. However, the DCOs have masses, sizes, and densities similar to the excess-light/central-cusps seen in typical elliptical galaxies with masses similar to the LBA galaxies. We suggest that the DCOs form in present-day examples of the dissipative mergers at high redshift that are believed to have produced the central-cusps in local ellipticals. More generally, the properties of the LBAs are consistent with the idea that instabilities in a gas-rich disk lead to very massive star-forming clumps that eventually coalesce to form a spheroid. We speculate that the DCOs are too young at present to be growing a supermassive black hole because they are still in a supernova-dominated outflow phase.
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