An undermount sink is installed beneath the stone countertop, usually by glueing the lips of the sink basin to the bottom of the countertop and otherwise strapping or supporting it. A drop-in sink, conversely, is set down into the countertop with its rim over the edge of the granite. With both, you need to be careful to prevent moisture or grime build-up inside the seam. Each style has its own unique advantages, which you should consider when choosing a style.
Maintains the continuous flow of the granite for a kind of “infinity pool” effect
Modern, clean feel
Weight of sink easily supported by strong materials like granite or marble
Maximum ease of cleaning counters and keeping surface germ-free
Usually provides for a deeper basin
Better resale value for your home
Granite rim is not exposed to chipping
Can accommodate vintage, specialty, or heirloom sinks
Generally less expensive than undercount sinks
Faucets do not need to be cut into the countertop or wall
Does not require professional installation
Bear in mind that when you get new stone countertops, part of the installation is cutting you a hole for your sink basin. Though it can be difficult to retro-fit a countertop with an undermount sink because it needs to be exactly the right size, it’s much easier to do when you install both parts simultaneously.