Morel’s $\mathbb{A}^1$-degree, which is a generalization of the Brouwer degree, is a fundamental tool in the application of motivic homotopy theory to enumerative geometry. A natural question to ask is how the $\mathbb{A}^1$-degree behaves under field extensions and transfers. This question is completely answered for separable field extensions (due to joint work with Brazelton, Burklund, Montoro, and Opie) and for simple extensions in dimension 1 (recent joint work with Brazelton). We will discuss what is known about this problem, as well as remaining open questions.