We give a comprehensive study on regularized approximate electromagnetic
cloaking via the transformation optics approach. The following aspects are
investigated: (i) near-invisibility cloaking of passive media as well as
active/radiating sources; (ii) the existence of cloak- busting inclusions
without lossy medium lining; (iii) overcoming the cloaking-busts by employing a
lossy layer outside the cloaked region; (iv) the frequency dependence of the
cloaking performances. We address these issues and connect the obtained
asymptotic results to singular ideal cloaking.