I will review the applications, advantages, limitations, and current status of harmonic techniques to detect anisotropies in the UHECR arrival direction distribution. In particular I will focus on the harmonic cross-correlation between the UHECR sky and galaxies, where the latter are taken as proxies for the locations of UHECR sources in the assumption that such sources correlate with the large-scale structure of the Universe. This type of harmonic cross-correlation has been proposed only recently, and it shows very promising complementarities with the well-known harmonic UHECR autocorrelation. After a brief introduction I will discuss novel tools and applications to account for different UHECR chemical composition and for the random deflections caused by the galactic magnetic field. I will show how the combination of UHECR harmonic auto-correlation and cross-correlations with large-scale structures can disentangle different UHECR primaries and could reverse-engineer some of the effects of the galactic magnetic field to a much better degree than the auto-correlation alone. I will conclude with an outlook on applications to other data sets, such as astrophysical neutrinos.