Quantum turbulence in superfluids appears as a stochastic tangle of quantized vortex lines. Interest to this system extends beyond the field of superfluid helium to include a large variety of topics both fundamental and engineering problem. In the article we present a discussion of the hot topic, which is undoubtedly mainstream in this field, and which deals with the quasi-classical properties of quantum turbulence. The idea that classical turbulence can be modeled by a set of slim vortex tubes (or vortex sheets) has been discussed for quite a long time. In classical fluids, the concept of thin vortex tubes is a rather fruitful mathematical model. Quantum fluids, where the vortex filaments are real objects, give an excellent opportunity for the study of the question, whether the dynamics of a set of vortex lines is able to reproduce (at least partially) the properties of real hydrodynamic turbulence. The main goal of this article is to discuss the current state of this activity. We cover such important topics as theoretical justification of this model, and experimental and numerical evidence for quasi-classical turbulence.