"Plasmon-based nanophotnics, an explosively growing research field concerned with surface-plasmon waveguides and circuitry, is oriented towards exploiting unique perspectives opened for radiation guiding along metal surfaces: extreme mode confinement (i.e., far beyond the diffraction limit) and seamless interfacing of electronic and photonic circuits (that both utilize the same metal circuitry). At the same time, unavoidable radiation absorption by metals results in the fundamental trade-off between the mode confinement and propagation loss, so that the problem of making the most of the above unique features becomes of paramount importance. The proposal encompasses two ground-breaking research directions in plasmonics that explore and utilize extremely confined plasmon-waveguide modes for functional and quantum nanophotonics. These directions of in-depth investigations concentrate within two interrelated and largely unexplored research areas within plasmonics: development of ultra-compact plasmonic configurations exhibiting unique functionalities and realization of strong coupling between extremely confined plasmonic modes and individual quantum emitters. Fundamental studies of ultimate mode confinement and coupling to quantum emitters would evolve into investigations carried out within forefront topics including (i) dynamic control of plasmon-waveguide modes using the same metal circuitry for both radiation guiding and its control with electrical signals; (ii) moulding the radiation flow by gradually varying waveguide cross sections in order to realize efficient nanofocusing of radiation, miniature ultra-dispersive wavelength-selective components and table-top models of plasmonic black holes, and (iii) quantum plasmonics with individual quantum emitters being strongly coupled to deep subwavelength surface plasmon modes, targeting the realization of a saturable waveguide mirror, single-photon transistor and long-distance entanglement of two remote quantum emitters."