Although the existence of magnetic monopoles is admitted by​​the fundamental laws, the real monopoles in nature remain elusive.​​Nevertheless, monopoles can appear in realistic condensed​​matter systems, from quantum Hall effects​to ​​topological​​superconductivity​, which spur a race to discover new exotic​ ​topological phases of matter. In this talk, we will present dramatic effects ​arising from topological​Fermi surface​s -- a novel topological class of superconductivity and density-wave orders​: ​When​the ordered pairs acquire​​non-trivial two-particle Berry phases, their pairing phases cannot be​well-defined globally in the momentum space. Therefore, the​ conventional description of superconducting pairing symmetries in​ terms of spherical harmonics (e.g. s-, p-, d-waves) ceases to apply.​ Instead, they are characterized by topologically protected nodal gap functions represented by monopole harmonic functions. This “monopole harmonic order” is expected to be realized and be detected in Weyl semimetal materials.