  We present a detailed experimental and theoretical study of the effect of
nuclear spin on the performance of optical lattice clocks. With a state-mixing
theory including spin-orbit and hyperfine interactions, we describe the origin
of the $^1S_0$-$^3P_0$ clock transition and the differential g-factor between
the two clock states for alkaline-earth(-like) atoms, using $^{87}$Sr as an
example. Clock frequency shifts due to magnetic and optical fields are
discussed with an emphasis on those relating to nuclear structure. An
experimental determination of the differential g-factor in $^{87}$Sr is
performed and is in good agreement with theory. The magnitude of the tensor
light shift on the clock states is also explored experimentally. State specific
measurements with controlled nuclear spin polarization are discussed as a
method to reduce the nuclear spin-related systematic effects to below
10$^{-17}$ in lattice clocks.
