Quadrilaterals are shapes that have four sides. They can be classified based on their angles or pairs of sides. Some common types of quadrilaterals are rectangles, which have four right angles, squares which are rectangles with four equal sides, rhombi which have four equal sides but not necessarily right angles, and trapezoids which have only one pair of parallel sides. The key difference between a square and rhombus is that a square has four right angles while a rhombus does not necessarily have right angles.