After a brief historical perspective on the three-nucleon ($3N$) interaction, we will focus on the chiral $3N$ forces and discuss some of the main present discrepancies with experimental data on low-energy $p-d$ scattering. By including the subleading $3N$ contact interactions, expected to arise at the fifth order of the chiral expansion (N4LO), these discrepancies can be solved. However, part of the needed contributions can be regarded as fourth-order (N3LO), because they are induced by a unitary transformation devised to absorb redundant $NN$ contact interactions at N3LO. As a result, a satisfactory description in $NN$ and $3N$ systems can be achieved already at N3LO. Finally, the pionless case will be described, with particular emphasis on the different treatment of the $3N$ force, and on possible consequences for the chiral series.