Stochastic models with irreversible elementary processes are introduced, and their macroscopic behaviors in the infinite-time and infinite-volume limits are studied extensively, in order to discuss nonequilibrium stationary states and phase transitions. The Domany-Kinzel model is a typical example of such an irreversible particle system. We first review this model, and explain that in a certain parameter region, the nonequilibrium phase transitions it exhibits can be identified with directed percolation transitions on the spatio-temporal plane. We then introduce an interacting particle system with particle conservation called friendly walkers (FW). It is shown that the m = 0 limit of the correlation function of m friendly walkers gives the correlation function of the Domany- Kinzel model, if we choose the parameters appropriately. We show that FW can be considered as a model of interfacial wetting transitions, and that the phase transitions and critical phenomena of FW can be studied using Fisher's theory of phase transitions in linear systems. The FW model may be the key to constructing a unified theory of directed percolation transitions and wetting transitions. Descriptions of FW as a model of interacting vicious walkers and as a vertex model are also given.