Let $\mathbb{F}_q$ be a finite field with $q$ elements and denote by $θ: \mathbb{F}_q\to\mathbb{F}_q$ an automorphism of $\mathbb{F}_q$. In this paper, we deal with skew constacyclic codes, that is, linear codes of $\mathbb{F}_q^n$ which are invariant under the action of a semi-linear map $Φ_{α,θ}:\mathbb{F}_q^n\to\mathbb{F}_q^n$, defined by $Φ_{α,θ}(a_0,...,a_{n-2}, a_{n-1}):=(αθ(a_{n-1}),θ(a_0),...,θ(a_{n-2}))$ for some $α\in\mathbb{F}_q\setminus\{0\}$ and $n\geq 2$. In particular, we study some algebraic and geometric properties of their dual codes and we give some consequences and research results on $1$-generator skew quasi-twisted codes and on MDS skew constacyclic codes.