Themis is an old and statistically robust asteroid family populating the outer main belt, and resulting from a catastrophic collision that took place 2.5 ± 1.0 Gyr ago. Within the old Themis family a young sub-family, Beagle, formed less than 10 Myr ago, has been identified. We present the results of a spectroscopic survey in the visible and near infrared range of 22 Themis and 8 Beagle families members. The Themis members investigated exhibit a wide range of spectral behaviors, including asteroids with blue/neutral and moderately red spectra, while the younger Beagle family members look spectrally bluer than the Themis ones and they have a much smaller spectral slope variability. Four Themis members, including (24) Themis, have absorption bands centered at 0.68–0.73 μμm indicating the presence of aqueously altered minerals. The best meteorite spectral analogues found for both Themis and Beagle families members are carbonaceous chondrites having experienced different degrees of aqueous alteration, prevalently CM2 but also CV3 and CI, and some of them are chondrite samples being unusual or heated. The presence of aqueous altered materials on the asteroids surfaces and the meteorite matches indicate that the parent body of the Themis family experienced mild thermal metamorphism in the past.We extended the spectral analysis including the data available in the literature on Themis and Beagle families members, and we looked for correlations between spectral behavior and physical parameters using the albedo and size values derived from the WISE data. The analysis of this larger sample confirms the spectral diversity within the Themis family and that Beagle members tend to be bluer and to have an higher albedo. The differences between the two families may be partially explained by space weathering processes, which act on these primitive surfaces in a similar way than on S-type asteroids, i.e. producing reddening and darkening. However we see several Themis members having albedos and spectral slopes similar to the young Beagle members. Alternative scenarios are proposed including heterogeneity in the parent body having a compositional gradient with depth, and/or the survival of projectile fragments having a different composition than the parent body.