Living cells are hierarchically self-organized forms of active soft matter: molecules on the nanometer scale form functional structures and organelles on the micron scale, which then compose cells on the scale of 10s of microns. While the biological functions of intracellular organelles are defined by the composition and properties of the structures themselves, how those bulk properties emerge from the properties and interactions of individual molecules remains poorly understood. Actin, a globular protein which self-assembles into dynamic semi-flexible polymers, is the basic structural material of cells and the major component of many functional organelles. In this thesis, I have used purified actin as a model system to explore the interplay between molecular-scale dynamics and organelle-scale functionality, with particular focus on the role of molecular-scale non-equilibrium activity., One of the most canonical forms of molecular-scale non-equilibrium activity is that of mechanoenzymes, also called motor proteins. These proteins utilized the free energy liberated by hydrolysis of ATP to perform mechanical work, thereby introducing non-equilibrium "active" stresses on the molecular scale. Combining experiments with mathematical modeling, we demonstrate in this thesis that non-equilibrium motor activity is sufficient to drive self-organization and pattern formation of the multimeric actin-binding motor protein Myosin II on 1D reconstituted actomyosin bundles., Like myosin, actin is itself an ATPase. However, nono-equilibrium ATP hydrolysis on actin is known to regulate the stability and assembly kinetics of actin filaments rather than generate active stresses per se. At the level of single actin filaments, the inhomogeneous nucleotide composition generated along the filament length by hydrolysis directs binding of regulatory proteins like cofilin, which mediate filament disassembly and thereby accelerate actin filament turnover. The concequences of this non-equilibrium turnover on the steady-state properties of collections of filaments remained unclear. Here, I reconstituted tunable, non-equilibrium actin turnover dynamics in entangled solutions of actin filaments as a model of the actin cortex of living cells. We found that this non-equilibrium turnover decouples solution mechanics from microstructure, enabling structurally indistinguishable materials to behave effectively as either viscous fluids or elastic gels. Additionally, we employed computer simulations to identify the dynamical regime in which actin turnover controls the effective viscosity of 2D cross-linked actin networks in the presence of motors., Additionally, I examine in this thesis the localization and self-assembly of actin filaments in condensed liquid phases called polyelectrolyte coacervates as a model membrane-less organelle. We find that concentration of actin through spontaneous partitioning preferentially to the coacervate phase accelerates the assembly of filaments. These filaments then localize to the coacervate-bulk interface, generating particles with visco-elastic shells surrounding liquid cores. In this case, the properties of the condensed phase enable regulation of actin assembly dynamics.