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Various cosmological models in frames of $F(T)$ gravity are considered. Thegeneral scheme of constructing effective dark energy models with variousevolution is presented. It is showed that these models in principle arecompatible with $\Lambda$CDM model. The dynamics of universe governed by $F(T)$gravity can mimics $\Lambda$CDM evolution in past but declines from it in afuture. We also construct some dark energy models with the "real"(non-effective) equation-of-state parameter $w$ such that $w\leq-1$. It isshowed that in $F(T)$ gravity the Universe filled phantom field not necessarilyends its existence in singularity. There are two possible mechanisms permittingthe final singularity. Firstly due to the nonlinear dependence between energydensity and $H^{2}$ ($H$ is the Hubble parameter) the universe can expands notso fast as in the general relativity and in fact Little Rip regime take placeinstead Big Rip. We also considered the models with possible bounce in future.In these models the universe expansion can mimics the dynamics with futuresingularity but due to bounce in future universe begin contracts.

Effective Dark Energy Models and Dark Energy Models with Bounce in frames of $F(T)$ Gravity