Transport of nanoparticles affects applications ranging from targeted drug delivery to enhanced oil recovery to processing of nanocomposite materials. In each of these applications, nanoparticles must be transported through a complex fluid to reach the desired target, whether a cancerous tumor, the oil-water interface, or a polymer melt. For large particles, the surrounding medium is effectively homogeneous across the surface of the particle, so that the transport properties can be directly related to the bulk fluid properties. For nanoparticles, however, the particle size is comparable to the length scales of heterogeneities in the fluid so that the particle dynamics decouple from bulk properties and are poorly understood. Here, we combine microscopy and scattering experiments with molecular simulation to investigate how nanoparticles transport through two models of complex fluids: polymer solutions, which model viscoelastic liquids, and supercooled and glassy colloidal liquids, which model crowded suspensions. In each setting, we probe how the dynamics of the nanoparticles are coupled to relaxations of the surrounding liquid. The physics elucidated in these studies will grant better control over the transport and dispersion of nanoparticles through complex, heterogeneous materials.