  In this paper, we study some Euler-Ap\'ery-type series which involve central
binomial coefficients and (generalized) harmonic numbers. In particular, we
establish elegant explicit formulas of some series by iterated integrals and
alternating multiple zeta values. Based on these formulas, we further show that
some other series are reducible to ln(2), zeta values, and alternating multiple
zeta values by considering the contour integrals related to gamma functions,
polygamma functions and trigonometric functions. The evaluations of a large
number of special Euler-Ap\'ery-type series are presented as examples.
