Professor Hamkins already gave many interesting references. Let me add a few more.
Possibly, the work of Cummings-shelah Cardinal invariants above the continuum is the starting point for the study of generalizations of cardinal invariants to the context of uncountable cardinals. In this paper, they prove the following: If $λ↦(β(λ),δ(λ),μ(λ))$ is a class function from regular cardinals into the cube of cardinals satisfying $λ^+≤β(λ)=cf(β(λ))≤cf(δ(λ))≤δ(λ)≤μ(λ)$ and $cf(μ(λ))>λ$ for all $λ$, then there exists a model where $b(λ)=β(λ), \mathfrak{d}(λ)=δ(λ)$, and $2^λ=μ(λ)$ for all $λ$.
for some other references see