The selection of suitable tailored variational wavefunctions is a fundamental problem in the study of quantum many-body systems. Variational approaches based on tensor networks are a novel powerful numerical tool believed to be the key ingredient to simulate efficiently quantum-many body systems. Among the proposed tensor networks, a very promising one is the so-called Multiscale Entanglement Renormalization Ansatz (MERA). I will discuss how to extract the critical exponents from the MERA ansatz and apply the method to a number of one-dimensional spin models.