We propose two types of full three-dimensional subwavelength surface-plasmon-polariton cavities: a metal-coated dielectric nanowire with an axial heterostructure and dielectric nanodisk/metal nanopan structure. In the metal-coated dielectric nanowire plasmonic structure, surface plasmon-polaritons are strongly confined at the nanowire-metal interface sandwiched by a plasmonic mirror structure that consists of nanowire core/low-index shell/metal shell. High quality factors and subwavelength mode volumes are calculated in this plasmonic structure. In addition, we report the experimental demonstration of an optically-pumped plasmonic lasing action from an InP nanodisk/silver nanopan structure with a subwavelength mode volume. A whispering-gallery plasmonic mode is excited at the bottom of the silver nanopan structure. We believe that these subwavelength plasmonic cavities and lasers represent a significant step towards the realization of faster and smaller coherent light sources which are suitable for an ultracompact nanophotonic integrated circuit.