Another short one today.
The images say it all.

Figure 1. The giant rat (genus: Coryphomys) compared to an extant rat of typical size.
Some rodents grew really big
(by comparison to their modern counterparts). We have a giant rat (genus: Coryphomys, Fig. 1) and a giant capybara (genus: Josephoartigasia, Fig. 2; Rinderknecht & Blanco 2008), the size of a cow. The largest living rodent is the capybara (genus: Hydrochoerus). One might say it is the size of a pig with a skull larger than a human skull.

Figure 2. Josephoartigasia monesi dwarfs the largest extant rodent, Hydrochoerus, the capybara. That skull is 53cm long.
The giant squirrel,
Ratufa (Fig. 3; extant) at 36 cm snout/vent length is the size of a small dog.

Figure 2. Ratufa, giant Indian squirrel skeleton and in vivo image. Note the large, cat-like claws and compare them to the smaller claws on all related taxa.
References
Aplin et al. 2010. Quaternary Murid Rodents of Timor Part I: New Material of Coryphomys buehleri Schaub, 1937, and Description of a Second Species of the Genus. Bulletin of the American Museum of Natural History, 2010; 3411 DOI: 10.1206/692.1
Aplin KP and Helgen KM 2010. Quaternary murid rodents of Timor part I: new material of Coryphomys buehleri Schaub, 1937, and description of a second species of the genus. Bulletin of the American Museum of Natural History. 341: 1–80. doi:10.1206/692.1
Braun J, Mares M, Coyner B and Van Den Bussche R 2010. New species of Akodon (Rodentia: Cricetidae: Sigmodontinae) from central Argentina. Journal of Mammalogy, 91 (2), 387-400 DOI: 10.1644/09-MAMM-A-048.1
CSIRO Australia. Archaeologists discover biggest rat that ever lived: Weight of about 6 kilograms (over 13 lb). ScienceDaily. ScienceDaily, 26 July 2010.
Rinderknecht A, Blanco RE 2008. “The largest fossil rodent”. Proceedings of the Royal Society B. 275 (1637): 923–8.
https://en.wikipedia.org/wiki/Josephoartigasia_monesi