Models for irreversible random or cooperative filling of lattices are required to describe many processes in chemistry and physics. Since the filling is assumed to be irreversible, even the stationary, saturation state is not in equilibrium. The kinetics and statistics of these processes are described by recasting the master equations in infinite hierarchial form. Solutions can be obtained by implementing various techniques involving, e.g., truncation or formal density expansions. Refinements in these solution techniques are presented;Problems considered include random dimer, trimer, and tetramer filling of 2D lattices, random dimer filling of a cubic lattice, competi- tive filling of two or more species, and the effect of a random distribu- tion of inactive sites on the filling. We also consider monomer filling of a linear lattice with nearest neighbor cooperative effects and solve for the exact cluster-size distribution for cluster sizes up to the asymptotic regime. Additionally, we develop a technique to directly determine the asymptotic properties of the cluster-size distribution;Finally, we consider cluster growth via irreversible aggregation involving random walkers. In particular, we provide explicit results for the large-lattice-size asymptotic behavior of trapping probabilities and average walk lengths for a single walker on a lattice with multiple;traps. Procedures for exact calculation of these quantities on finite lattices are also developed; *DOE Report IS-T-1230. This work was performed under Contract W-7405-eng-82 with the Department of Energy.