We describe the Very Small Array (VSA) and review the recent results on the angular power spectrum of the Cosmic Microwave Background (CMB) obtained in the Ka-band (ν ≈ 33 GHz) with this instrument. This array has covered an ℓ-range of 150 to 1500 with a relatively high resolution in ℓ compared to previous measurements at ℓ≥ 1000; this is achieved by using mosaiced observations in 7 regions covering a total of approximately 82 sq. degrees. Our resolution of Δ ℓ ≈ 60 between ℓ=300 and ℓ = 1500 allows the first 3 acoustic peaks to be identified. Contamination by extragalactic radiosources brighter than 20 mJy has been taken into account by simultaneously monitoring identified sources with a high resolution interferometer. In addition, it has been performed a statistical correction for the small residual contribution from weaker sources that are below this flux limit. There is good agreement between the VSA power spectrum and that obtained by WMAP and other higher resolution experiments like ACBAR and CBI. We have set constraints on cosmological parameters using VSA data and combinations with other CMB data and external priors. Within the flat ΛCDM model, the combined VSA+WMAP data without external priors gives Ω_{b}h^2=0.0234^{+0.0012}_{-0.0014}, Ω_{dm}h^2=0.111^{+0.014}_{-0.016}, h=0.73^{+0.09}_{-0.05}, n_{S}=0.97^{+0.06}_{-0.03}, 10^{10}A_{S}=23^{+7}_{-3} and τ=0.14^{+0.14}_{-0.07}. We also find evidence for a running spectral index of density fluctuations, n_{run}=-0.069± 0.032 at a level of more than 95% confidence. However, inclusion of prior information from the 2dF galaxy redshift survey reduces the significance of the result. When a general cosmological model with 12 parameters is considered we find consistency with other analyses available in the literature. The evidence for n_{run}<0 is only marginal within this model. The fraction of dark matter in neutrinos is constrained to f_{ν}< 0.087 (95% confidence limit) which implies that m_ν<0.32 eV if all the three neutrino species have the same mass.