This is not very recent but it is worth mentioning. One approach to the existence of category of mixed motives $MM(k)$ ($k$ a field of characteristic zero) is via the existence of the motivic Galois group $\mathbf{G}_{mot}(k)$ since $MM(k)$ is expected be a neutral Tannakian category. One candidate of such a group is the Nori motivic Galois group, $\mathbf{G}_{Nori}(k)$. There is a different approach by Ayoub when $k \subset \mathbb{C}$, called the *weak Tannakian formalism*. Let me recall some general nonsense: let $(\mathcal{M},\mathbf{1},\otimes), (\mathcal{N},\mathbf{1},\otimes)$ be two symmetric monoidal category and $f \colon \mathcal{M} \to \mathcal{N}$ a symmetric monoidal functor having a right adjoint $g \colon \mathcal{N} \to \mathcal{M}$.

**Theorem** (Ayoub). *Assume that there exists a monoidal functor $e \colon \mathcal{N} \to \mathcal{M}$ such that $f \circ e \simeq id_{\mathcal{N}}$ and $e$ has a right adjoint $u$ and furthermore the coprojection $g(A) \otimes M \simeq g(A \otimes f(M))$ is an isomorphism, then the object $fg\mathbf{1}$ is a Hopf algebra*.

Let's denote by $\mathbf{DA}(k,\mathbb{Q})$ the category of étale motives with rational coefficients, and
$$(\operatorname{Bti}^* \dashv \operatorname{Bti}_*) \colon \mathbf{DA}(k,\mathbb{Q}) \longrightarrow \mathbf{D}(\mathbb{Q})$$ the Betti realization, where $\mathbf{D}(\mathbb{Q})$ is the derived category of $\mathbb{Q}$-vector spaces. Since $\operatorname{Bti}^*$ has a section given by sending a $\mathbb{Q}$-vector space $V$ to the constant presheaf with values in $V$. The theorem above can be applied to this situation to endow $H=\operatorname{Bti}^*\operatorname{Bti}_*\mathbf{1}$ a Hopf algebra structure and Ayoub showed furthermore that $H$ has no homology in negative degree, so it is a $\mathbb{Q}$-Hopf algebra. The scheme $\operatorname{Spec}(H)$ is called the *Ayoub motivic Galois group* $\mathbf{G}_{Ayoub}(k)$. The magic thing is

**Theorem** (Choudhurry, Gallauer, Souza). $\mathbf{G}_{Ayoub}(k) \simeq \mathbf{G}_{Nori}(k)$.

So at least, theoretically, we have one more reason to believe that this is a candidate for the real motivic Galois group.