||Mammalian hosts have evolved protein "restriction factors" to combat retroviruses. TRIM5α and the related TRIMCyp protein (collectively TRIM5), are restriction factors that can potently restrict retroviruses, including HIV-1, by binding their capsids and blocking reverse transcription. Previous studies have shown that the C-terminal SPRY/CypA domains of TRIM5 proteins bind the capsids of susceptible retroviruses and that higher-order oligomerization of TRIM5 proteins apparently also contributes to capsid binding. However, the biochemical and structural details of these interactions are not fully understood. To study how TRIM5 proteins recognize capsids, we have developed new methods for expressing and purifying recombinant TRIM5 proteins. Here, we report biochemical, electron microscopic and X-ray crystallographic studies of pure recombinant TRIM5 proteins and their complexes with authentic HIV-1 core particles and in vitro-assembled mimics of the HIV-1 capsid surface. In Chapter 2, we report the expression, purification and electron crystallographic studies of a restrictive, but non-native chimeric rhesus TRIM5 protein (TRIM5-21R), and show that TRIM5-21R can spontaneously self-assemble into paracrystalline hexagonal lattices comprising 6-sided rings. Moreover, ring assembly is promoted by TRIM5-21R binding to hexagonal HIV-1 CA assemblies. In Chapter 3, we report the first crystal structure of a TRIM coiled-coil domain (from human TRIM25) as well as supporting analytical ultracentrifugation and disulfide crosslinking experiments showing that other iv TRIM coiled-coils, including TRIM5, also form antiparallel dimers that are ~170 Å long. In Chapter 4, we describe the expression and purification of 11 different mammalian TRIM5 alleles. We demonstrate that TRIM5 hexagonal assembly is a conserved property and report electron microscopic and biochemical studies showing that TRIM5 proteins form a ~35 nm-spaced, flexible hexagonal "net" on the surface of decorated HIV-1 cores and other capsid mimics. In Chapter 5, I present my ongoing attempts to crystallize and determine the structure of the TRIM5α core domains in the assembled state. Taken together, my work supports a "pattern recognition" model for capsid recognition in which TRIM5 proteins have evolved to restrict a variety of different retroviruses by cooperatively assembling flexible hexagonal nets that can bind avidly and adapt to the symmetry, hexagonal spacing and curvature of retroviral capsids.