In this contribution, I will focus on the evolutionary histories of irregular (Irr) and dwarf irregular (dIrr) galaxies, including their chemical evolution. The name "irregular" refers to the irregular, amorphous appearance of these galaxies at optical wavelengths, where the light contribution tends to be dominated by scattered bright HII regions and their young, massive stars. Irrs are typically gas-rich galaxies that lack spiral density waves as well as a discernible bulge or nucleus. Many Irrs are disk galaxies and appear to be an extension of late-type spirals. The most massive disky Irrs with residual spiral structure are also called Magellanic spirals; e.g., the Large Magellanic Cloud (LMC) (Kim et al. 1998) is a barred Magellanic spiral. Looser and more amorphous Irrs like the Small Magellanic Cloud (SMC) are sometimes also referred to as Magellanic irregulars (or barred Magellanic irregulars if a bar is present); see de Vaucouleurs (1957). A different system of subdivisions was suggested by van den Bergh in his DDO luminosity classification system (van den Bergh 1960, 1966). DIrrs are simply less massive, less luminous Irrs; the distinction between the two is a matter of definition rather than physics. Typical characteristics of dIrrs are a central surface brightness µV 23 mag arcsec-2, a total mass of Mtot 1010 M, and an HI mass of MHI 109 M. Solid body rotation is common among the Irrs and more massive dIrrs, while low-mass dIrrs do not show measurable rotation; here random motions dominate. A typical characteristic of Irrs and dIrrs alike is ongoing or recent star formation. The star formation intensity may range from burst-like, strongly enhanced activity, to slow quiescent episodes. Irrs and dIrrs can continue to form stars over a Hubble time (Hunter 1997).
Substantial progress has been made in the photometric exploration of the star formation histories of Irrs and dIrrs over the past decade, largely thanks to the superior resolution of the Hubble Space Telescope. There is still very little known about the progress of the chemical evolution in these galaxies as a function of time, but the advent of 6-m to 10-m class telescopes and their powerful spectrographs is beginning to change this situation. The most detailed information is available for nearby Irr and dIrr galaxies in the Local Group, most notably the LMC, which is the Irr galaxy closest to the Milky Way.