Recently there have been renewed interest and relevant progress in calculating overlaps between periodic multiparticle states and integrable boundary states. They appear in quite distinct parts of theoretical physics including statistical physics and the gauge/string duality. I will give a summary of known overlap formulas and analyze the connection between selection rules and symmetries. I will introduce a nesting procedure for boundary states which provides the factorizing overlaps for higher rank algebras automatically. This method can be used for the calculation of the asymptotic all-loop 1-point functions in AdS/dCFT. In doing so I will present the solutions of the YBE for the K-matrices with centrally extended su(2|2) symmetry and the generic overlaps of the corresponding boundary states. Based on 2004.11329 ------------------------- Part of London Integrability Journal Club. Please register at integrability-london.weebly.com/ for the zoom link