In this paper, necessary and sufficient conditions of the one-sided reverse order law (ab) # = b # a # , the two-sided reverse order law (ab) # = b # a # and (ba) # = a # b # for the core inverse are given in rings with involution. In addition, the mixed-type reverse order laws, such as (ab) # = b # (abb #) # , a # = b(ab) # and (ab) # = b # a # , are also considered.