In this talk, I will discuss joint work with Levi Haunschmid-Sibitz where we construct the stochastic six-vertex model speed process. We will first define the stochastic six-vertex model with step initial data and show that a second-class particle started at the origin converges almost surely to an asymptotic speed. We will then generalize this by assigning each particle in the model a different class, allowing us to simultaneously track the speeds of all the particles. The speed process is obtained as the joint limit of these speeds. Along the way, we will develop a stochastic domination result for second- and third-class particles, as well as moderate deviation tail bounds for the stochastic six-vertex model