Magnetically connected socket joint components comprise one or more paired components so as to form socket joint structures which can form various different articles, such as, for example, articles of jewelry, toys, educational implements, games or amusement devices, instructional aids, eyeglass frames, robotic arms, prosthetic devices, human replacement joints, and the like. The socket joint structures comprise convexly configured male and concavely configured female socket components which may be fabricated from suitable magnetic materials, or alternatively, the convexly configured male socket components may be fabricated from suitable magnetic materials while the concavely configured female socket components may be fabricated from suitable ferromagnetic materials, or vice versa.