Acid copolymers and ionomers are polymers that contain a small fraction of covalently bound acidic or ionic groups, respectively. For the specific case of polyethylene (PE), acid and ionic pendants enhance many of the physical properties such as toughness, adhesion and rheological properties. These improved properties result from microphase separated aggregates of the polar pendants in the non-polar PE matrix. Despite the widespread industrial use of these materials, rigorous chemical structure - morphology - property relationships remain elusive due to the inevitable structural heterogeneities in the historically-available acid copolymers and ionomers. Recently, precise acid copolymers and ionomers were successfully synthesized by acyclic diene metathesis (ADMET) polymerization. These precise materials are linear, high molecular weight PEs with pendant acid or ionic functional groups separated by a precisely controlled number of carbon atoms. The morphologies of nine precise acid copolymers and eleven precise ionomers were investigated by X-ray scattering, solid-state 13C nuclear magnetic resonance (NMR) and differential scanning calorimetry (DSC). For comparison, the morphologies of linear PEs with pseudo-random placement of the pendant groups were also studied. Previous studies of precise copolymers with acrylic acid (AA) found that the microstructural precision produces a new morphology in which PE crystals drive the acid aggregates into layers perpendicular to the chain axes and presumably at the interface between crystalline and amorphous phases. In this dissertation, a second new morphology for acid copolymers is identified in which the aggregates arrange on cubic lattices. The fist report of a cubic morphology was observed at room and elevated temperatures for a copolymer functionalized with two phosphonic acid (PA) groups on every 21st carbon atom. The cubic lattice has been identified as face-centered cubic (FCC). Overall, three morphology types have been identified for precise acid copolymers and ionomers at room temperature: (1) liquid-like order of aggregates dispersed throughout an amorphous PE matrix, (2) one-dimensional long-range order of aggregates in layers coexisting with PE crystals, and (3) three-dimensional periodicity of aggregates in cubic lattices in a PE matrix featuring defective packing. The liquid-like morphology is a result of high content of acid or ionic substituents deterring PE crystallinity due to steric hindrance. The layered morphology occurs when the content of pendants is low and the PE segments are long enough to crystallize. The cubic morphologies occur in precise copolymers with geminal substitution of phosphonic acid (PA) groups and long, flexible PE segments. At temperatures above the thermal transitions of the PE matrix, all but one material present a liquid-like morphology. Those conditions are ideal to study the evolution of the interaggregate spacing (d*) in X-ray scattering as a function of PE segment length between pendants, pendant type and pendant architecture (specifically, mono or geminal substitution). Also at elevated temperatures, the morphologies of precise acrylic acid (AA) copolymers and ionomers were investigated further via atomistic molecular dynamics (MD) simulations. The simulations complement X-ray scattering by providing real space visualization of the aggregates, demonstrating the occurrence of isolated, string-like and even percolated aggregate structures. This is the first dissertation completely devoted to the morphology of precise acid copolymers and precise ionomers. The complete analysis of the morphologies in these novel materials provides new insights into the shapes of aggregates in acid copolymers and ionomers in general. A key aspect of this thesis is the complementary use of experimental and simulation methods to unlock a wealth of new understanding.