In this talk we will discuss the properties of integrable discrete nonlinear equations on quadrilateral lattices, containing bosonic and fermionic fields. As a basic working example we will focus on the super-H1 equation (which in the continuum limit goes to supersymmetric Korteweg de Vries system) and we will show how to implement the cubic consistency (a special symmetry related to integrability) and super-Lax pairs. Also, the dynamics of super-soliton solutions and resolution of singularities will be discussed together with the geometry of invariants.