  In this paper we present some new identities for multiple polylogarithms
(abbr. MPLs) and multiple harmonic star sums (abbr. MHSSs) by using the methods
of iterated integral computations of logarithm functions. Then, by applying
these formulas obtained, we establish some explicit relations between
Kaneko-Yamamoto type multiple zeta values (abbr. K-Y MZVs), multiple zeta
values (abbr. MZVs) and MPLs. Further, we find some explicit relations between
MZVs and multiple zeta star values (abbr. MZSVs). Furthermore, we define an
Ap\'{e}ry-type variant of MZSVs $\zeta^\star_B({\bf k})$ (called multiple zeta
$B$-star values, abbr. MZBSVs) which involve MHSSs and central binomial
coefficients, and establish some explicit connections among MZVs, alternating
MZVs and MZBSVs by using the method of iterated integrals. Finally, some
interesting consequences and illustrative examples are presented.
