The talk will address two aspects of the connection between nonequilibrium molecular-level processes and properties of actin related to cell motility. 1) The effects of ATP hydrolysis on force generation and polymerization dynamics. Using an extended Brownian-ratchet methodology, it is shown that hydrolysis of bound nucleotide can reduce the stall force of ensembles of actin filaments by a factor of three or more relative to the thermodynamic stall force. The force reduction occurs because the interaction with the obstacle induces hydrolysis at the tip, which converts filament tips temporarily to a depolymerizing state. It is also shown that hydrolysis can lead to overshoots in actin polymerization traces. The overshoots occur when the characteristic time of polymerization is shorter than the nucleotide exchange time on monomers. This effect may be present in cells with sufficiently high concentrations of free barbed ends. 2) The effects of network structure on the contractile stress generated by active myosin II interacting with actin filaments. Using elasticity theory combined with an effective-medium theory, it is shown that the stress generated per myosin is proportional to the average filament length. This leads to estimates of the cytokinesis tension that are much lower than existing estimates. unless the filaments are bundled into inextensible units longer than a filament. Continued contraction requires treadmilling of actin filaments, and the rate of contraction is limited by the filament treadmilling rate.