Slow

A slow is a type of status effect that reduces the afflicted units movement speed by a percentage, and/or attack speed by a flat value of their current speeds.

Mechanics
Usually, slows from different sources stack with each other, but multiple of the same instance do not, but refresh their duration instead. There are some exceptions to this.

Slowing movement speed
Movement speed slows are always percentage based. The percentage of multiple slow instances fully stack, following this movement speed formula. A unit's movement speed cannot be slowed below 100, as it is the minimum allowed movement speed. The only exception are some trap abilities, which set affected units' movement speed to 0. Although roots disallow movement, they technically do not slow and thus have no influences on abilities which work with movement speed. Hexes do not slow either, but rather set a unit's base movement speed to a certain value.

A unit affected by haste fully ignores movement speed slows.

Slowing attack speed
Attack speed slows stack additively as well, but unlike movement speed, do not reduce attack speed by a percentage, but by a flat value. A unit's attack speed cannot be slowed below 20 (every unit's base attack speed is 100, except Roshan who starts with 200). There are no exceptions to this. Disarms do not slow attack speed, but simply do not allow affected units from attacking at all, so their attack speed value is unaffected.

There is no equivalent to haste for attack speed, although some abilities give an enormously high attack speed bonus, so that it is impossible to reduce their attack speed in a regular game.