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We present applications of microscopic models to nuclear reactions of astrophysical interest, and we essentially focus on few-body systems. The calculation of radiative-capture and transfer cross sections is outlined, and we discuss the corresponding reaction rates. Microscopic theories are briefly presented, and we emphasize on the matrix elements of four-body systems. The microscopic extension of the R-matrix theory to nuclear reactions is described. Applications to the 2H(d, γ)4He, 2H(d, p)3H and 2H(d, n)3He reactions are presented. We show the importance of the tensor force to reproduce the low-energy behaviour of the cross sections.