Computational aspects of irreducible polynomials

We present results on testing the computation of bounds for polynomial divisors and give estimates for their heights. There are also given results on the irreducibility of polynomials and some methods for constructing irreducible polynomials. They are based on properties of Newton's polygon. Finally we give applications to the irreducibility of univariate polynomials $F(X)=\sum\limits_{i = 0}^d{{a}_{i}}{{X}^{d- i}}$ over a discrete valuation domain. We give applications to bivariate polynomials.