  Superconducting Quantum Interference Devices (SQUIDs) are one of the most
popular devices in superconducting electronics. They combine the Josephson
effect with the quantization of magnetic flux in superconductors. This gives
rise to one of the most beautiful manifestations of macroscopic quantum
coherence in the solid state. In addition, SQUIDs are extremely sensitive
sensors allowing to transduce magnetic flux into measurable electric signals.
As a consequence, any physical observable that can be converted into magnetic
flux, e.g., current, magnetization, magnetic field or position, becomes easily
accessible to SQUID sensors. In the late 1980's it became clear that downsizing
the dimensions of SQUIDs to the nanometric scale would encompass an enormous
increase of their sensitivity to localized tiny magnetic signals. Indeed,
nanoSQUIDs opened the way to the investigation of, e.g., individual magnetic
nanoparticles or surface magnetic states with unprecedented sensitivities. The
purpose of this review is to present a detailed survey of microscopic and
nanoscopic SQUID sensors. We will start by discussing the principle of
operation of SQUIDs, placing the emphasis on their application as
ultrasensitive detectors for small localized magnetic signals. We will continue
by reviewing a number of existing devices based on different kinds of Josephson
junctions and materials, focusing on their advantages and drawbacks. The last
sections are left for applications of nanoSQUIDs in the fields of scanning
SQUID microscopy and magnetic particle characterization, putting special stress
on the investigation of individual magnetic nanoparticles.
