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I discuss some quantum aspects of the Skyrme-Faddeev (or the baby-Skyrme) type models. The well-known Skyrme model describes properties of hadrons after a suitable quantization is performed. The collective coordinate approximation is used to examine the spectra and several other properties of hadrons. The Wess-Zumino action obeys a quantization law of which the prefactor is the number of quark colors ({\it i.e.} of the degeneracy). $\mathbb{C}P^N$ Skyrme-Faddeev model possesses two-dimensional soliton solutions. For $N=1$ it is believed that the quantum aspects exhibit a special property, so called the fractional spin $\frac{\theta}{2\pi}~(0\leq \theta \leq \pi)$, when the Hopf term is added in the action of the model. For the point of view of a fermionic model coupled with the baby-skyrmions, however, no ambiguity by $\theta$ appears. An analogue of the Wess-Zumino term appears in $\mathbb{C}P^N$ field which plays a similar role as the Hopf term, and now the soliton has to be quantized as an anyon even if a fermionic model is taken into account. I would like to discuss the issues through the heat kernel expansion and also the spectral flow analysis.

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