The first evidences for magnetic activity in low-mass protostars and brown dwarfs were found in the mid-1990's by the old generation of X-ray satellites, namely ROSAT and ASCA. I will show that these first X-ray detections have opened a promising observational window to study the activity of protostars, deeply embedded in their molecular cloud and optically invisible. However these early observations gave only access to the tip of the iceberg, detecting protostars mainly during phases of high activity. I will review recent results obtained with the new generation of X-ray satellites, namely Chandra and XMM-Newton, which now give access to the X-ray spectral study of protostars also during their quiescent phase, and which are also enough sensitive to detect young brown dwarfs in star-forming regions. I will also review evidences of activity from radio observations, and for brown dwarfs, evidences of activity from optical observations.