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The first fast radio burst (FRB) to be precisely localized was associated with a luminous persistent radio source (PRS). Recently, a second FRB/PRS association was discovered for another repeating source of FRBs. However, it is not clear what makes FRBs or PRS or how they are related. We compile FRB and PRS properties to consider the population of FRB/PRS sources. We suggest a practical definition for PRS as FRB associations with luminosity greater than 10²⁹erg s⁻¹Hz⁻¹that are not attributed to star formation activity in the host galaxy. We model the probability distribution of the fraction of FRBs with PRS for repeaters and nonrepeaters, showing there is not yet evidence for repeaters to be preferentially associated with PRS. We discuss how FRB/PRS sources may be distinguished by the combination of active repetition and an excess dispersion measure local to the FRB environment. We use CHIME/FRB event statistics to bound the mean per-source repetition rate of FRBs to be between 25 and 440 yr⁻¹. We use this to provide a bound on the density of FRB-emitting sources in the local universe of between 2.2 × 10²and 5.2 × 10⁴Gpc⁻³assuming a pulsar-like beamwidth for FRB emission. This density implies that PRS maymore »comprise as much as 1% of compact, luminous radio sources detected in the local universe. The cosmic density and phenomenology of PRS are similar to that of the newly discovered, off-nuclear “wandering” active galactic nuclei (AGN). We argue that it is likely that some PRS have already been detected and misidentified as AGN.

The physical properties of fast radio burst (FRB) host galaxies provide important clues towards the nature of FRB sources. The 16 FRB hosts identified thus far span three orders of magnitude in mass and specific star formation rate, implicating a ubiquitously occurring progenitor object. FRBs localized with ∼arcsecond accuracy also enable effective searches for associated multiwavelength and multi-time-scale counterparts, such as the persistent radio source associated with FRB 20121102A. Here we present a localization of the repeating source FRB 20201124A, and its association with a host galaxy (SDSS J050803.48+260338.0, z = 0.098) and persistent radio source. The galaxy is massive (${\sim}3\times 10^{10}\, \text{M}_{\odot }$), star-forming (few solar masses per year), and dusty. Very Large Array and Very Long Baseline Array observations of the persistent radio source measure a luminosity of 1.2 × 1029 erg s−1 Hz−1, and show that is extended on scales ≳50 mas. We associate this radio emission with the ongoing star formation activity in SDSS J050803.48+260338.0. Deeper, high-resolution optical observations are required to better utilize the milliarcsecond-scale localization of FRB 20201124A and determine the origin of the large dispersion measure (150–220 pc cm−3) contributed by the host. SDSS J050803.48+260338.0 is an order of magnitude more massive than any galaxy or stellar system previously associated with a repeating FRB source, butmore »is comparable to the hosts of so far non-repeating FRBs, further building the link between the two apparent populations.