The paper introduces a new class of three-dimensional (3D) topological phases, called higher-order topological insulators (HOTIs), which exhibit gapless hinge states protected by spatiotemporal symmetries. Two specific cases are discussed: (i) Chiral higher-order topological insulators, protected by time-reversal and a fourfold rotation symmetry, with chiral hinge modes and a Z2-classified bulk topology. (ii) Helical higher-order topological insulators, protected by time-reversal and mirror symmetries, with Kramers-paired hinge states and a Z-classified bulk topology. The authors provide topological invariants for both cases and propose SnTe as a material realization for helical HOTIs, along with an experimental setup to detect the hinge states. The study also discusses the possibility of chiral HOTIs in 3D TI materials with noncollinear antiferromagnetic order.The paper introduces a new class of three-dimensional (3D) topological phases, called higher-order topological insulators (HOTIs), which exhibit gapless hinge states protected by spatiotemporal symmetries. Two specific cases are discussed: (i) Chiral higher-order topological insulators, protected by time-reversal and a fourfold rotation symmetry, with chiral hinge modes and a Z2-classified bulk topology. (ii) Helical higher-order topological insulators, protected by time-reversal and mirror symmetries, with Kramers-paired hinge states and a Z-classified bulk topology. The authors provide topological invariants for both cases and propose SnTe as a material realization for helical HOTIs, along with an experimental setup to detect the hinge states. The study also discusses the possibility of chiral HOTIs in 3D TI materials with noncollinear antiferromagnetic order.