We review some recent results concerning with the existence of positive solutions of the following problem \begin{cases} \displaystyle -\Delta u +H(x,u,\nabla u)= \lambda f(u) \quad & \mbox{in}\,\, \Omega, \\ u=0 &\mbox{on} \, \partial \Omega, \end{cases} where f is a continuous nonnegative function in [0,+\infty) with f(0)>0 and H is a Carathédory function defined on \Omega\times [0,+\infty)\times \mathbb{R}^{N}. Specifically, we show how this problem provides a general framework to study Gelfand type problems. We give sufficient conditions to prove that there exists \lambda^*>0 such that the problem has a minimal solution u_\lambda provided that 0\leq \lambda<\lambda^* and no solution if \lambda >\lambda^*. We pay special interest in the extension of the classical stability condition as well as a general comparison principle.