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Part of Special Issue: Oxide superconductors and beyond - In memoriam of Professor Karl Alex Müller, Abstract: Discovery of high-Tc cuprate superconductors (HTSC) in 1986 by Bednorz and Muller, followed by synthesis of A3C60, iron-pnictides/chalcogenides and other exotic superconducting (SC) systems, introduced unconventional superconductors (UCSC) having their mechanisms of condensation and/or pairing distinctly different from those of simpler metals which can be explained by BCS theory. This article will show how one can demonstrate their new mechanisms by examining correlations among key energy-scale parameters, including the transition temperature Tc, the superfluid density ns/m*, the effective Fermi energy εF, the excitation energy of the magnetic resonance mode (MRM), the onset temperatures of Nernst effect and light-induced transient superconductivity, and the spin fluctuation energy scale ℏωsf, and by resorting to analogy / comparisons with superfluid 4He as a representative system undergoing Bose Einstein Condensation (BEC). We will propose a paring mechanism in HTSC based on resonance of spin (ℏωsf) and charge (εF) energy scales, and apply that concept for explaining unusual behaviors in the overdoped region. We will also discuss modifications of a simple BEC-BCS crossover picture to account for actual situations with additional effects of competing order and phase separation.