In this chapter, we are concerned with the study of the spectrum of some differential nonhomogeneous operators with one or several variable exponents. We establish results that are no longer valid in the case of homogeneous operators. Essentially, these new results are possible due to the gap between the infimum and the maximum of the nonconstant exponents. The analysis carried out in this chapter takes into account the two possible Rayleigh quotients associated to these problems. The content of this chapter is related to the papers [52, 54, 56, 27, 70, 65, 66, 69, 71].