|Integrable PDEs are characterized by many interesting properties, one
of which is the existence of multi-soliton solutions. The construction
of these solutions is particularly simple using Hirota's direct
method. It turns out that although many equations have one and even
two-soliton solutions, the existence of three-soliton solutions is in
practice equivalent to integrability. This provides a method for
searching for integrable equations. We briefly review the situation in
the continuum case and present some new results in the discrete case.