Dwarf irregular (dIr) galaxies are frequent targets of young stellar populations research. But less attention has been devoted to their intermediate-age and old stars. For galaxies at moderate distances (more than ~ 10 Mpc) the study of these populations must rely on population sinthesys techniques that provide just crude estimates. For nearby galaxies, carbon stars and planetary nebulae are usual indicators of the presence of intermediate-age stars, since RR Lyrae proof the existence of an old population. Having stars in those evolutionary phases is enough evidence for such populations, but they don't provide the actual fraction of stars in each age interval and hence, the quantitative SFH. This can be obtained from the information contained in the color-magnitude (CM) diagram. The best and most reliable source of information is the distribution of stars in the main sequence (MS), which can also show turn-offs tracing single star formation bursts. In general, the position, spread and luminosity function of the MS, combined with the information provided by the stellar evolution models and an asumption of the IMF is all we need to derive a reliable estimate of the SFH of the system. Unfortunately, for old stars, this technique can be only applied to the Magellanic Clouds and to the nearby dwarf spheroidal stellites of the Milky Way. For other galaxies and to distances about 4-5 Mpc ( 1.5 Mpc if ground based facilities are used), we must rely on evolved (RGB and AGB) stars to derive the old and intermediate-age SFH. In this case, monte-carlo methods are being used since the last few years to generate model CM diagrams for varying SFHs. This diagrams are based in a complete and reliable library of stellar evolution models and must include an accurate simulation of observational effects. When compared with the real observed diagrams, they give the way for determining the SFH since the oldest populations. In the present contribution, we shortly review the previous work devoted to the old and intermediate-age population in dIrs; summarize the techniques used to derive the SFH for those ages and show recent results of our group and others for the SFH (which includes both the star formation rate and the chemical evolution history) of nearby dIrs. These galaxies show evidences for a very old ( ~ 15 Gyr) star formation activity. Averaged to time intervals large enough (a few Gyr for the oldest stars) they show a decreasing SFR, a larger fraction of their stars having been formed during the first half of their lives than during the second.