Some background: All Chrysler's makes got new bodies for 1957. For the 1960 model year, all brands except Imperial were given new bodies featuring a form of unitized construction. I've yet to read an explanation for Imperial's exception, but I'll speculate that it had to do with wheelbase length and the task of modifying unit-bodies that was difficult compared to modification of body-on-frame cars. Chrysler New Yorkers had 126-inch wheelbases both before and after the changeover. Imperials had 129-inch wheelbases in 1959, but to have them share the new unitized bodies while maintaining the longer wheelbase would have been expensive for a brand that typically sold fewer than 20,000 cars per year. In other words, it was cheaper to continue the body-on-frame arrangement, especially because Imperials were already being assembled at their own factory on Warren Avenue in Dearborn -- a facility formerly used by Graham and DeSoto -- and therefore didn't need to be integrated into assembly lines for other Chrysler products.
This arrangement continued through the 1966 model year. Thereafter, Imperials were again derivations of Chryslers until the brand was phased out after 1975.
Wikipedia's Imperial entry refers to 1957-1966 models as the brand's "second generation," so scroll down the link for its take on those Imperials.
Unless otherwise noted, the images below are of cars posted for sale on various web sites.
The first year for the new body featured styling director Virgil Exner's beloved tailfins in their classic form. Tail lights are built into the fines, and those truncated chrome rings harken to the freestanding lights-in-rings introduced on 1955 Imperials. The spare tire faux-cover on the trunk lid is another holdover feature.
Rear styling was essentially unchanged for 1958
Some side chrome has been added, and interior detailing on the bumper is changed. The 1957-59 bumper shape disappears for 1960, but partly returns in 1964.
Imperials got a significant facelift for 1960. Tailfins were enlarged and reshaped, the bumper was redesigned and the spare tire "cover" was replaced by a simple chrome strip. Sedan back windows were also reshaped.
Aft sections of the tailfins were restyled again for 1961. Tail light assemblies are now freestanding, a side chrome strip has been added and some trunk/bumper area ornamentation changed. LeBaron sedans had smaller backlights than other Imperials.
Fins disappear for the 1962 model year, requiring yet another tail light restyling. Those torpedo-shaped tail light elements are functionally superfluous, only serving as a thematic link to previous Imperials. Returned is the faux spare tire cover. Also restyled is the bumper. The after part of the passenger greenhouse is redesigned in a more angular fashion, and the backlight has changed as well.
There were few changes for 1963. Gone are those torpedo-shaped tail light elements.
Now the influence of new styling director Elwood Engel finally kicks in with this facelift echoing Elwoods masterpiece 1961 Lincoln Continental. Everything abaft of the B-pillar has been changed. It will be seen better on following images but the aft end of the trunk lid sports a squared-off sort of spare tire cover. The bumper tapers towards the sides, harking to the 1957-59 shape. The medallion at the center can be considered the hub of the notional spare tire.
The design is essentially unchanged for 1965 other than the back window being replaced by a smaller unit.
This is the final model year for the 1957 body. At the rear, the only significant change is the elimination of the faux- spare tire "cover" -- now there is some squared-off shaping in the aft part of the trunk lid.