Lighting up/displaying vertices

How can I light up or simply display vertices of a mesh?

It would be nice if there was a possibility to light them up with a shader/material.

If the mesh isn’t procedurally created, but is a prefab or one of the built-in meshes, you can add a Mesh Particle System to your project and then select the mesh whose vertices you’d like to see as the target mesh of the Particle System’s Mesh Particle Emitter component. Leaving all velocities = 0, this causes all emitted particles to remain at the vertex positions. Perhaps playing with the colors and sizes of the particles will achieve the desired effect.