Running Pliers
When the edge of the glass is placed in the jaws and the center bump is set on the score line and pressed, the running pliers exert even pressure on both sides of the score line, making for an even break in the glass.
More expensive running pliers can be adjusted so that pressure on the glass can be changes, allowing for better results on different types of glass. There are also different types of surfaces inside the jaws themselves. Because of this, pricing on running pliers varies a lot - from $7 to around $100. If you are expecting to work with regular hobbyist glass for a while and don't expect to get into specialty or thick glass, you can stay on the lower end and have a perfectly usable product.