Mathematicians have been studying nonnegativity of real polynomials since as early as the 19th century. Nonnegativity certificates are an important tool in these investigations, giving easier to check, sufficient conditions for nonnegativity. In this talk we will motivate the study of nonnegativity by relating it to polynomial optimization. Furthermore, we will define the nonnegativity certificates sums of squares (SOS) and sums of nonnegative circuit polynomials (SONC).