We shall study first split-quaternions and then split-octonions. For technical reasons split-quaternions will be constructed by applying the Cayley-Dickson construction to complex numbers and split-octonions by applying this construction to quaternions. Our attention will be devoted to special elements and their properties in these two algebras. We shall classify all subalgebras in split-quaternions and split-octonions and further describe the types of isotropic subspaces in them.