Mechanical performances are the most important aspect of elastomers consisting of a three-dimensionally crosslinked polymer network. Dynamic properties such as toughness, self-recoverability, and self-healing ability can be implemented by incorporation of physical crosslinks, which are weak and reversible bonds or interactions, into polymer networks. In this review, we focus on elastomers having hydrogen bonds (H-bonds) as the physical crosslinks and discuss the recent advances and directions in the field. After a general introduction to physical crosslinks and H-bonds in polymeric materials, our study on a tough and self-recoverable elastomer based on bioinspired phase-separated structure is reviewed. Application of this strategy to triblock copolymer-type thermoplastic elastomers is also discussed in the following section. Then, we turn our attention to the chemistry of H-bonds and introduce our recent findings on a tough and self-healable elastomer based on a new class of H-bonds, namely the entropy-driven H-bonds. Finally, the current and future directions of the H-bonded polymeric materials are discussed.