LESS and Sass are CSS preprocessors that allow for variables, mixins, and nested rules to make CSS more maintainable. Some key differences are that LESS uses @variables while Sass uses $variables. Both support mixins but LESS calls them with .mixin() while Sass uses @include. Nesting rules in LESS and Sass avoids repetition by nesting selectors within parent elements. Both support math operations and functions to generate CSS values programmatically.