Using a combination of deep MID-IR observations obtained by IRAC, MIPS and IRS on board Spitzer we investigate the MID-IR properties of Lyman Break Galaxies (LBGs) at z~3, establish a better understanding of their nature and attempt a complete characterisation of the population. With deep mid-infrared and optical observations of ~1000 LBGs covered by IRAC/MIPS and from the ground respectively, we extend the spectral energy distributions (SEDs) of the LBGs to mid-infrared. Spitzer data reveal for the first time that the mid-infrared properties of the population are inhomogeneous ranging from those with marginal IRAC detections to those with bright rest-frame near-infrared colors and those detected at 24μm MIPS band revealing the newly discovered population of the Infrared Luminous Lyman Break Galaxies (ILLBGs). To investigate this diversity, we examine the photometric properties of the population and we use stellar population synthesis models to probe the stellar content of these galaxies. We find that a fraction of LBGs have very red colors and large estimated stellar masses M∗>5×1010M⊙. We discuss the link between these LBGs and submm-luminous galaxies and we report the detection of rest frame 6.2 and 7.7 μm emission features arising from Polycyclic Aromatic Hydrocarbons (PAH) in the Spitzer/IRS spectrum of an infrared-luminous Lyman break galaxy at z=3.01.