High temperature superconductivity is typically found in the vicinity of a magnetically ordered phase. The parent state of iron-based superconductors is most often a collinear antiferromagnet that breaks the tetragonal symmetry of the high temperature phase. Such a magnetically ordered state is accompanied by an orthorhombic lattice distortion and the nematic ordering of electronic degrees of freedom. Intriguingly, FeSe is an iron-based superconductor that realizes nematic ordering in the absence of any long range magnetic order. A recent scanning tunneling microscopy (STM) experiment deduced the superconducting gap structure of FeSe suggesting that in this material orbital selectivity plays a significant role in superconducting pairing. Within a multi-orbital Hubbard model for iron-based superconductors, such orbital selectivity is expected and driven by a sizable Hund's coupling. In this thesis, I use STM to visualize quasiparticle interference patterns in the unusual nematic state of FeSe. The analysis of these patterns demonstrates that the quasi-particle weight is significantly larger for the $d_{yz}$ orbitals than for the $d_{xz}$ and $d_{xy}$ orbitals. This establishes the existence of strong orbital-selective correlations in FeSe. Additionally, I identify significant directionality in the atomic structure of local density of states images in FeSe at low temperature. This is a novel method for visualizing nematicity in iron-based superconductors.