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Liquid crystal elastomers (LCEs) are composed of rod-like liquid crystal (LC) molecules (mesogens) linked into elastomeric polymer networks. They present a nematic phase with directionally ordered mesogens at room temperature and an isotropic phase with no order at high temperatures, enabling large thermal-induced deformation. As a result, LCEs have become promising candidates for new applications in soft robotics and shape morphing. LCEs are being actively studied in both experiment and theory in recent years. However, the fundamental relationship among synthesis, processing, and thermomechanical behaviors of modern LCEs are still largely unclear. This knowledge gap is further complicated by the various LCE types, including polydomain, monodomain, nematic-genesis, and isotropic-genesis, each fabricated and used under different experimental conditions and applications. Here we explore synthesis-processing-property relationships in thermomechanics of various LCEs, by combining fabrication, characterization, and theoretical modeling. We adapt the widely used two-stage method to fabricate isotropic-genesis polydomain LCEs and nematic-genesis LCEs with varying pre-stretches during polymerization. We characterize the thermal-induced spontaneous deformation and the temperature-dependent uniaxial stress-stretch responses of the LCEs. We identify a new relationship among the soft elasticity, the thermal-induced spontaneous deformation, and the pre-stretch during polymerization, in the LCEs under study. Building on classical theories and our experimental results, we develop a constitutive model to describe the uniaxial behaviors of various LCEs. The theoretical predictions agree well with the experimental results on uniaxial stress-stretch responses at different temperatures. Finally, we discuss the remaining challenges and future opportunities in synthesis-processing-property relationships of LCEs.