  Ground-based adaptive optics (AO) in the infrared has made exceptional
advances in approaching space-like image quality at higher collecting area.
Optical-wavelength applications are now also growing in scope. We therefore
provide here a comparison of the pros and cons of observational capabilities
from the ground and from space at optical wavelengths. With an eye towards the
future, we focus on the comparison of a ~30m ground-based telescope with an
8-16m space-based telescope. We review the current state-of-the-art in AO, and
summarize the expected future improvements in image quality, field of view,
contrast, and low-wavelength cut-off. We discuss the exciting advances in
extreme AO for exoplanet studies and explore what the theoretical limitations
in achievable contrast might be. Our analysis shows that extreme AO techniques
face both fundamental and technological hurdles to reach the contrast of 1E-10
necessary to study an Earth-twin at 10 pc. Based on our assessment of the
current state-of-the-art, the future technology developments, and the inherent
difficulty of observing through a turbulent atmosphere, we conclude that there
will continue to be a strong complementarity between observations from the
ground and from space at optical wavelengths in the coming decades. There will
continue to be subjects that can only be studied from space, including imaging
and (medium-resolution) spectroscopy at the deepest magnitudes, and the
exceptional-contrast observations needed to characterize terrestrial exoplanets
and search for biomarkers.
