Nodal geometry of Laplace eigenfunctions

Let $M$ be a compact Riemannian manifold and $\varphi_\lambda$ be an eigenfunction of the Laplacian corresponding to the eigenvalue $\lambda$. We will survey a few recent results in the area regarding the geometry of nodal sets and nodal domains of $\varphi_\lambda$. We will also mention joint work with Bogdan Georgiev and Stefan Steinerberger.