We present the current status of the QUIJOTE (Q-U-I JOint TEnerife) experiment, a new polarimeter with the aim of characterizing the polarization of the Cosmic Microwave Background, and other galactic or extra-galactic physical processes that emit in microwaves in the frequency range 10-42GHz, and at large angular scales (around 1 degree resolution). The experiment has been designed to reach the required sensitivity to detect a primordial gravitational wave component in the CMB, provided its tensor-to-scalar ratio is larger than r ∼ 0.05. The project consists of two telescopes and three instruments which will survey a large sky area from the Teide Observatory to provide I, Q and U maps of high sensitivity. The first QUIJOTE instrument, known as Multi-Frequency Instrument (MFI), has been surveying the northern sky in four individual frequencies between 10 and 20 GHz since November 2012, providing data with an average sensitivity of 80μKbeam-1 in Q and U in a region of 20,000 square-degrees. The second instrument, or Thirty-GHz Instrument (TGI), is currently undergoing the commissioning phase, and the third instrument, or Forty-GHz Instrument (FGI), is in the final fabrication phase. Finally, we describe the first scientific results obtained with the MFI. Some specific regions, mainly along the Galactic plane, have been surveyed to a deeper depth, reaching sensitivities of around 40 μK beam-1. We present new upper limits on the polarization of the anomalous dust emission, resulting from these data, in the Perseus molecular complex and in the W43 molecular complex.