We review knowledge about the roles of sex chromosomes in vertebrate hybridization and speciation, exploring a gradient of divergences with increasing reproductive isolation (speciation continuum). Under early divergence, well-differentiated sex chromosomes in meiotic hybrids may cause Haldane-effects and introgress less easily than autosomes. Undifferentiated sex chromosomes are more susceptible to introgression and form multiple (or new) sex chromosome systems with hardly predictable dominance hierarchies. Under increased divergence, most vertebrates reach complete intrinsic reproductive isolation. Slightly earlier, some hybrids (linked in 'the extended speciation continuum') exhibit aberrant gametogenesis, leading towards female clonality. This facilitates the evolution of various allodiploid and allopolyploid clonal ('asexual') hybrid vertebrates, where 'asexuality' might be a form of intrinsic reproductive isolation. A comprehensive list of 'asexual' hybrid vertebrates shows that they all evolved from parents with divergences that were greater than at the intraspecific level (K2P-distances of greater than 5-22% based on mtDNA). These 'asexual' taxa inherited genetic sex determination by mostly undifferentiated sex chromosomes. Among the few known sex-determining systems in hybrid 'asexuals', female heterogamety (ZW) occurred about twice as often as male heterogamety (XY). We hypothesize that pre-/meiotic aberrations in all-female ZW-hybrids present Haldane-effects promoting their evolution. Understanding the preconditions to produce various clonal or meiotic allopolyploids appears crucial for insights into the evolution of sex, 'asexuality' and polyploidy. This article is part of the theme issue 'Challenging the paradigm in sex chromosome evolution: empirical and theoretical insights with a focus on vertebrates (Part II)'.