This thesis considers coarse-grained models of DNA and RNA, developed in particular to study nanotechnological applications as well as some important biophysical processes. We first introduce sequence-dependent thermodynamics into a previously developed coarse-grained rigid base-pair model of DNA. This model is then used to study sequence-dependent effects in multiple DNA systems including: the heterogeneous stacking transition of single strands, the fraying of a duplex, the effects of stacking strength in the loop on the melting temperature of hairpins, the force-extension curve of single strands, and the structure of a kissing-loop complex. We further apply the DNA model to study in detail the properties of an autonomous unidirectionally propagating DNA nanotechnological device, called the ``burnt bridges motor''. We then apply the coarse-graining methods developed for the DNA model to construct a new sequence-dependent coarse-grained model of RNA, which aims to capture basic thermodynamic, structural and mechanical properties of RNA molecules. We test the model by studying its thermodynamics for a variety of secondary structure motifs and also consider the force-extension properties of an RNA duplex. This RNA model allows for efficient simulations of a variety of RNA systems up to hundreds or even thousands of base-pairs. Its versatility is further demonstrated by studying the thermodynamics of a pseudoknot folding, the formation of a kissing loop complex, the structure of a hexagonal RNA nanoring, and the unzipping of a hairpin.