Glossary
Records are problems presenting the largest/longest/biggest/... something. That's a vague definition !!
Records emphasize the sportive (also, scientific) aspect of chess composition, as opposed to the artistic side. Records are "beautiful" just because they are records, and then hard to compose.
In the field of chess composition, there exist hundreds of different records. Regularly, previous records are improved on (also, new records are invented). Some broad categories exist, to help organize this:
This WWW Retro Corner cannot survey the current state of all retro-records. Some of them are listed in a chapter of Karl Fabel's 1955 book Rund um das Schachbrett. This chapter is already quite old but the problems it contains are available here. Other sources include [Küh89] among many others.
Here is a length record from Fabel ([Q] has it been improved?):
Dr. Karl Fabel Am Rande des Schachbretts, 1947
13+11. Ortho-Reconstruction in 171.5 moves (Wh. starts)
I'll include the solution when some kind sould send it to me (please, use a PGN file).