  We study the symplectic Bott-Chern cohomology by L.-S. Tseng and S.-T. Yau
for solvmanifolds endowed with left-invariant symplectic structures. Our
results are applicable to cohomology with values in local systems. Studying
symplectic Bott-Chern cohomology of solvmanifolds with values in local systems,
we give some remarks on symplectic Hodge theory.
