We extend some classical results of Bankwitz, Crowell, and Murasugi to the
setting of virtual links. For instance, we show that an alternating virtual
link is split if and only if it is visibly split, and that the Alexander
polynomial of any almost classical alternating virtual link is alternating. The
first result is a consequence of an inequality relating the link determinant
and crossing number for any non-split alternating virtual link. The second is a
consequence of the matrix-tree theorem of Bott and Mayberry. We extend the
first result to semi-alternating virtual links. We discuss the Tait conjectures
for virtual and welded links and note that Tait's second conjecture is not true
for alternating welded links.