  We theoretically study time-resolved photoemission in atoms as probed by
attosecond streaking. We review recent advances in the study of the
photoelectric effect in the time domain and show that the experimentally
accessible time shifts can be decomposed into distinct contributions that stem
from the field-free photoionization process itself and from probe-field induced
corrections. We perform accurate quantum-mechanical as well as classical
simulations of attosecond streaking for effective one-electron systems and
determine all relevant contributions to the time delay with attosecond
precision. In particular, we investigate the properties and limitations of
attosecond streaking for the transition from short-ranged potentials
(photodetachment) to long-ranged Coulomb potentials (photoionization). As an
example for a more complex system, we study time-resolved photoionization for
endohedral fullerenes $A$@$\text{C}_{60}$ and discuss how streaking time shifts
are modified due to the interaction of the $\text{C}_{60}$ cage with the
probing infrared streaking field.
