  Pyrochlore lattices, which are found in two important classes of materials --
the $A_2B_2X_7$ pyrochlore family and the $AB_2X_4$ spinel family -- are the
quintessential 3-dimensional frustrated lattice architecture. While
historically oxides ($X =$~O) have played the starring role in this field, the
past decade has seen material's synthesis breakthroughs that have lead to the
emergence of fluoride ($X =$~F) and chalcogenide ($X =$~S, Se) pyrochlore
lattice materials. In this Research Update, we summarize recent progress in
understanding the magnetically frustrated ground states in three families of
non-oxide pyrochlore lattice materials: (i) $3d$-transition metal fluoride
pyrochlores, (ii) rare earth chalcogenide spinels, and (iii) chromium
chalcogenide spinels with a breathing pyrochlore lattice. We highlight how the
change of anion may modify the single ion spin anisotropy due to crystal
electric field effects, stabilize new magnetic atom combinations, or
dramatically alter the exchange pathways and thereby lead to new magnetic
ground states. We also consider a slate of future directions -- materials with
the potential to define the next decade of research in frustrated magnetism.
