The physics of condensed-matter nanosystems exhibits remarkable analogies with atomic nuclei. Examples are: Plasmons corresponding to Giant resonances , electronic shells, de- formed shapes, and fission , beta-type decay, strongly correlated phenomena associated with symmetry breaking and symmetry restoration , etc. Most recently, analogies with relativistic quantum-field theories (RQFT) and high-energy particle physics are beeing explored in the field of graphene nanostructures . The talk will review these analogies focusing in particular on the following three aspects: (1) The shell-correction method (SCM, commonly known as Strutinsky’s averaging method and introduced in the 1960’s in nuclear physics) was formulated  in the context of density functional theory (DFT). Applications of the DFT-SCM (and of a semiempirical variant, SE-SCM, closer to the nuclear Strutinsky approach) to condensed-matter finite systems will be discussed, including the charging and fragmentation of metal clusters, fullerenes, and metallic nanowires . The DFT-SCM offers an improvement compared to the use of Thomas-Fermi gradient expansions for the kinetic energy density functional in the framework of orbital-free DFT. (2) A unified description of strongly correlated phenomena in finite systems of repelling particles [whether electrons in quantum dots (QDs) or ultracold bosons in rotating traps] has been achieved through a two-step method of symmetry breaking at the unrestricted Hartree- Fock (UHF) level and of subsequent symmetry restoration via post Hartree-Fock projection techniques . The general principles of the two-step method can be traced to nuclear theory (Peierls and Yoccoz) and quantum chemistry (L ̈owdin). This method can describe a wide variety of novel strongly correlated phenomena, including: (I) Chemical bonding and dissociation in quantum dot molecules and in single elliptic QDs, with potential technological applications to solid-state quantum computing. (II) Particle localization at the vertices of concentric polygonal rings and formation of rotating (and other less symmetric) Wigner molecules in quantum dots and ultracold rotating bosonic clouds . (III) At high magnetic field (electrons) or rapid rotation (neutral bosons), the method yields analytic trial wave functions in the lowest Landau level , which are an alternative to the fractional-quantum-Hall-effect (FQHE) composite-fermion and Jastrow-Laughlin approaches. (3) The physics of planar graphene nanorings with armchair edge terminations shows analo- gies with the physics described by the RQFT Jackiw-Rebbi model and the related Su-Schrieffer- Heeger model of polyacetylene . This part of the talk will describe the emergence of exotic states and properties, like solitons, charge fractionization, and nontrivial topological insulators, in these graphene nanosystems.  C. Yannouleas, R.A. Broglia, M. Brack, and P.F. Bortignon, Phys. Rev. Lett. 63, 255 (1989);  C. Yannouleas, U. Landman, and R.N. Barnett, in Metal Clusters, edited by W. Ekardt (John-Wiley, New York, 1999) Ch. 4, p. 145;  C. Yannouleas and U. Landman, Rep. Prog. Phys. 70, 2067 (2007), and references therein;  I. Romanovsky, C. Yannouleas, and U. Landman, Phys. Rev. B 87, 165431 (2013); Phys. Rev. B 89, 035432 (2014).  C. Yannouleas and U. Landman, Phys. Rev. B 48, 8376 (1993); Ch. 7 in ”Recent Advances in Orbital-Free Density Functional Theory,” Y.A. Wang and T.A. Wesolowski Eds. (Word Scientific, Singapore, 2013) p. 203 (arXiv:1004.3536);  C. Yannouleas and U. Landman, Phys. Rev. Lett. 82, 5325 (1999); I. Romanovsky, C. Yannouleas, and U. Landman, Phys. Rev. Lett. 97, 090401 (2006).  C. Yannouleas and U. Landman, Phys. Rev. A 81, 023609 (2010); Phys. Rev. B 84, 165327 (2011).