Deflection of CR's can happen on many places. Progressing outward, these are: (1) the Geo-magnetosphere, (2) the Solar System environment (3) the interstellar medium (ISM) in our vicinity of the Galactic (Milky Way) disk, (4) the Galactic halo and metagalactic environment, the (5) the intergalactic environment within a few Mpc, and out to Centaurus A at 3.8 Mpc, (6) extragalactic space out to approximately a GZK radius, (7) the larger z Universe out to z 2.
In this presentation I ignore zones (1) and (2), and begin with the Milky Way's disk's environment. Here the general magnetic field strength is typically 2 - 5 µG and the local Galactic spiral arm cross section dimension is ~ 2 - 3 kpc. This curved, "magnetized tube" extends over ~ 10 kpc in the plane of the Galactic disk. However within the disk there are many magnetized gaseous systems such as old supernova remnant (SNR) shells and HII regions. Fields within these systems are locally much higher than 5 µG.
Beginning at 100 Mpc, that is in distance "zone" (7) we encounter large galaxy clusters. These are the largest gravitationally bound systems in the Universe, and magnetic fields their intra-cluster medium, (ICM), ~ 1Mpc in total size, are relatively well-measured at ~ 3 - 5 µG. This is comparable with the Milky Way disk, but in thermal ionized plasma densities of 10-2 - 10-3 cm-3, which is 2 - 3 orders of magnitude less than in the Milky Way disk. Significantly, the ICM energy densities are comparable to those of the ISM, because the ICM gas temperature is 2 - 3 orders of magnitude higher than that of the ISM.
Galaxy clusters are less relevant for our study of UHECR's for two reasons. (a) the gyroradii of UHECR protons in the ICM is less than the cluster radii, so that they remain captured within the cluster while losing much of their energy through radiation and p-p collisions with thermal ICM protons. (b) Galaxy clusters occupy a very small fraction of the intergalactic volume, so they are seldom encountered by HE particles and photons propagating through the general intergalactic medium (IGM).
Except for the galaxy clusters, less is known about the magnetic field strength and structure in (4) - (7) above. However probes are continuously improving, and these are discussed here. Also, HE photons and CR's themselves can probe the intergalactic magnetic field strength, for example though particle-photon cascades, propagation time delays, and measurable particle deflections.
In the following I give an overview of what we know about magnetic field strengths in the various distance régimes (3) - (7) mentioned above.