  Nanometer-scale imaging of magnetization and current density is the key to
deciphering the mechanisms behind a variety of new and poorly understood
condensed matter phenomena. The recently discovered correlated states hosted in
atomically layered materials such as twisted bilayer graphene or van der Waals
heterostructures are noteworthy examples. Manifestations of these states range
from superconductivity, to highly insulating states, to magnetism. Their
fragility and susceptibility to spatial inhomogeneities limits their
macroscopic manifestation and complicates conventional transport or
magnetization measurements, which integrate over an entire sample. In contrast,
techniques for imaging weak magnetic field patterns with high spatial
resolution overcome inhomogeneity by measuring the local fields produced by
magnetization and current density. Already, such imaging techniques have shown
the vulnerability of correlated states in twisted bilayer graphene to
twist-angle disorder and revealed the complex current flows in quantum Hall
edge states. Here, we review the state-of-the-art techniques most amenable to
the investigation of such systems, because they combine the highest magnetic
field sensitivity with the highest spatial resolution and are minimally
invasive: magnetic force microscopy, scanning superconducting quantum
interference device microscopy, and scanning nitrogen-vacancy center
microscopy. We compare the capabilities of these techniques, their required
operating conditions, and assess their suitability to different types of source
contrast, in particular magnetization and current density. Finally, we focus on
the prospects for improving each technique and speculate on its potential
impact, especially in the rapidly growing field of two-dimensional (2D)
materials.
