Domain walls naturally arise whenever a symmetry is spontaneously broken. They interconnect regions with different realizations of the broken symmetry, promoting structure formation from cosmological length scales to the atomic level ^1,2 . In ferroelectric and ferromagnetic materials, domain walls with unique functionalities emerge, holding great promise for nanoelectronics and spintronics applications ^3-5 . These walls are usually of Ising, Bloch or Néel type and separate homogeneously ordered domains. Here we demonstrate that a wide variety of new domain walls occurs in the presence of spatially modulated domain states. Using magnetic force microscopy and micromagnetic simulations, we show three fundamental classes of domain walls to arise in the near-room-temperature helimagnet iron germanium. In contrast to conventional ferroics, the domain walls exhibit a well-defined inner structure, which - analogous to cholesteric liquid crystals - consists of topological disclination and dislocation defects. Similar to the magnetic skyrmions that form in the same material ^6,7 , the domain walls can carry a finite topological charge, permitting an efficient coupling to spin currents and contributions to a topological Hall effect. Our study establishes a new family of magnetic nano-objects with non-trivial topology, opening the door to innovative device concepts based on helimagnetic domain walls.