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Notes: Abstract We review the results from recent deep HST imaging on faint galaxies. Artificial Neural Networks (ANNs) were used to classify faint galaxies based on surface brightness and light profiles. We use available UV + ground-basedU-band images of nearby galaxies to address the effects from the uncertain red shifted UV-morphology on the classifications, resulting in `restframe ANN' classifiers. These distinguish quite consistently between E/S0's, Sabc's, and Sd/Irr for B ≲ 27 mag. A Fourier-based method is used to quantify higher order morphological features and asymmetries in faint galaxies. We review the faint blue galaxy population as classified with these restframe ANN's. The median scale-length at B ∼ 27 mag is r hl≃ 0″.25-0″.3 (∼ 1-2 kpc at z ≃ 1-2). Early and late-type galaxies are fairly well separated in BVI color-magnitude diagrams for B≲27 mag, with E/S0's being the reddest and Sd/Irr's generally blue. We discuss the B-band galaxy counts as a function of type for 18.5 ≲ B≲ 28 mag. We briefly review deep medium-band imaging with HST/WFPC2 in the filter F410M(Lyα at z ≃ 2.4) which yielded 18 faint, compact objects surrounding the radio galaxy 53W002 at z ≃ 2.39, as well as another 30 in random HST parallel fields, plus ground-based images over a larger area. Deep HST/PC images of 53W002 at ∼ 0″.06 FWHM resolution in BVI + redshiftedLyαsuggest that both reflected AGN continuum-light shining through a cone and jet-induced star-formation play a role in its `alignment effect'. We discuss the formation and evolution of 53W002 in the context of its many surrounding sub-galactic sized objects. We discuss the nature of a μJy radio source that remained essentially unidentified in HDF flanking fields. The object was identified in deep HST/NICMOS J- and H-band images, and a single emission line at 6595 Å was detected, most likely Lyα at z=4.42. This faint (H =23.9 mag), compact (r e ≃ 0″.2), red (I-K = 2.0 mag) object is most likely a dusty, star-forming young galaxy with an embedded active nucleus. Finally, HST/NICMOS images are presented of some of the oldest known red galaxies at z ≃ 1.5.Both galaxies are dominated by a r 1/4-profile with 5 kpc scale-length, and are amongst the oldest known relaxed systems at that epoch.