  We present selected known results and some of their improvements, involving
Gurarii spaces. A Banach space is Gurarii if it has certain natural extension
property for almost isometric embeddings of finite-dimensional spaces. Deleting
the word "almost", we get the notion of a strong Gurarii space. There exists a
unique (up to isometry) separable Gurarii space, however strong Gurarii spaces
cannot be separable. The structure of the class of non-separable Gurarii spaces
seems to be not very well understood. We discuss some of their properties and
state some open questions. In particular, we characterize non-separable Gurarii
spaces in terms of skeletons of separable subspaces, we construct a
non-separable Gurarii space with a projectional resolution of the identity and
we show that no strong Gurarii space can be weakly Lindel\"of determined.
