Is there a standard reference for the theory (if it exists) of $\mathcal{V}$enriched locally presentable categories? Here $\mathcal{V}$ is a cosmos. Does anything unexpected happens here in contrast to the case $\mathcal{V}=\text{Set}$ treated in "Locally Presentable And Accessible Categories" by Adamek & Rosicky? In particular I'm interested in the case $\mathcal{V} = \text{Cat}$.
The standard reference is this paper by Max Kelly. Perhaps the most unexpected thing is how well the theory works! 


The theory is also developed further in two papers by Borceux, Quinteiro and Rosický: Enriched accessible categories MR1419612 and A theory of enriched sketches MR1624638. In the second one they say that they are particularly interested in case $\mathcal{V} = \text{Cat}$ and that they "intend to study this in a further publication", but I don't know of such a publication. 

