Colloidal lead halide perovskite nanocrystals (LHP NCs, NCs, A=Cs+, FA+, FA=formamidinium; X=Cl, Br, I) have become a research spotlight owing to their spectrally narrow (<100 meV) fluorescence, tunable over the entire visible spectral region of 400-800 nm, as well as facile colloidal synthesis. These NCs are attractive single-photon emitters as well as make for an attractive building block for creating controlled, aggregated states exhibiting collective luminescence phenomena. Attaining of such states through the spontaneous self-assembly into long-range ordered superlattices (SLs) is a particularly attractive avenue. In this regard also the atomically-flat, sharp cuboic shape of LHP NCs is of interest, because vast majority of prior work had invoked NCs of rather spherical shape. Long-range ordered SLs with the simple cubic packing of cubic perovskite NCs exhibit sharp red-shifted lines in their emission spectra and superfluorescence (a fast collective emission resulting from coherent multi-NCs excited states). When CsPbBr3 NCs are combined with spherical dielectric NCs, perovskite-type ABO3 binary NC SLs form, wherein CsPbBr3 nanocubes occupy B- and/or O-sites, while with spherical dielectric Fe3O4 or NaGdF4 NCs reside on A-sites. When truncated-cuboid PbS NCs are added to these systems, ternary ABO3-phase form (PbS NCs occupy B-sites). Such ABO3 SLs, as well as other newly obtained SL structures (binary NaCl, AlB2- and ABO6 types, columnar assemblies with disks etc.), exhibit a high degree of orientational ordering of CsPbBr3 nanocubes. These mesostructures exhibit superfluorescence as well, characterized, at high excitation density, by emission pulses with ultrafast (22 ps) radiative decay and Burnham-Chiao ringing behaviour with a strongly accelerated build-up time. Combining CsPbBr3 nanocubes with large and thick NaGdF4 nanodisks results in the orthorhombic SL resembling CaC2 structure with pairs of CsPbBr3 NCs on one lattice site. We also implement two substrate-free methods of SL formation. Oil-in-oil templated assembly and self-assembly at the liquid–air interface result in the formation of binary supraparticles.