Copyrights do expire. Works eventually enter the public domain and may be freely used. Current laws extend copyright protection for the life of the author plus 70 years. Laws have changed over the years, so you would need to find what law was in effect when a work was created to determine if that work is still protected.
Alice in Wonderland (Illustrator: Winter, 1924) Mad Tea Party
Copyright: Public Domain
Digital Rights: Copyright Toronto Public Library
Source Credit: Toronto Public Library (Osborne)