Many designs were prompted by the desire to expand the off-road capabilities of land-vehicles to an "all-terrain" ability, in some cases not only focused on creating a transport that will work on land and water, but also on intermediates like ice, snow, mud, marsh, swamp etc. This explains why many designs use tracks in addition to or instead of wheels, and in some cases even resort to articulated body configurations or other unconventional designs such as screw-propelled vehicles which use auger-like barrels which propel a vehicle through muddy terrain with a twisting motion.
Most land vehicles even lightly armoured ones can be made amphibious simply by providing them with a waterproof hull and perhaps a propeller. This is possible as a vehicle's displacement is usually greater than its weight, and thus it will float. Heavily armoured vehicles however sometimes have a density greater than water (their weight in kilograms exceeds their volume in litres) and will need additional buoyancy measures. These can take the form of inflatable floatation devices, much like the sides of a rubber dinghy, or a waterproof fabric skirt raised from the top perimeter of the vehicle, to increase its displacement.