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

Alternating multiple zeta values, and explicit formulas of some Euler-Apery-type series