Plastics are the most versatile and high-performance materials available today. Most traditional plastics feature high molecular weight polymers that rely on entanglement, intermolecular interactions, and/or cross-links to provide desirable mechanical properties. In many polymers, the strong covalent bonds that endow impressive properties also extend polymer lifetimes and limit opportunities for modification. As plastics continue to permeate into nearly every sector of our global economy including healthcare, packaging, and technology, new polymers are required to enable new functions. Dynamic processes such as bond exchange chemistry, thermodynamic reversibility, and improved segmental motion impart functionality to these next-generation materials. Herein, we design, develop, and study new dynamic polymer systems for three intended applications: (1) thermoset reprocessing; (2) chemical recycling to monomer; and (3) polymer electrolytes for lithium-ion batteries. First, we design and study a class of dynamic poly(ester-imine)s and demonstrate their strong mechanical properties and reprocessability (Chapter 2). We synthesize five linear polyester terpolymers of varying compositions and use a diamine cross-linker to form poly(ester-imine) networks. In all cases, we achieve polymer networks with high tensile strengths that are maintained over multiple reprocessing cycles. We also observe that cross-link distribution in the polymer networks impacts the thermomechanical behavior of the materials at elevated temperatures. Next, we demonstrate that poly(1,3-dioxolane) (PDXL) is a tough thermoplastic capable of chemical recycling to monomer (Chapter 3). During the cationic ring-opening polymerization of cyclic acetals, our reversible-deactivation polymerization strategy allows access to targeted molecular weights and gives high living chain-end retention. We reveal that PDXL is a tough, ductile polymer with good thermal stability and viable applications. We also show that PDXL undergoes efficient depolymerization to monomer in the presence of a strong acid, even from a mixture of commodity plastics. In Chapter 4, we synthesize a series of five polyacetals with varying oxygen to carbon ratios in the polymer backbone and compare their performance to the predominant polymer electrolyte, PEO. We measure conductivity and current fraction for each polyacetal at a range of lithium bis(trifluoromethylsulfonylimide) (LiTFSI) concentrations. At the same salt concentration, we reveal that ionic conductivity decreases approximately four-fold while the current fraction increases nearly five times with increasing oxygen to carbon ratio. By calculating the polymer efficacy, we identify two polyacetals with improved performance as compared to PEO. In Chapter 5, we use a combination of spectroscopy and molecular dynamics to study both cation and anion diffusivity in the series of polyacetals and PEO. We attribute the trends in conductivity and current fraction to decreasing segmental motion of the polymer chains and ionic clustering, respectively.