A drill that spins beautifully but won't hold a bit is one of the most frustrating tool faults in DIY, and one of the most consistently misdiagnosed. The chuck is doing the work of three small jaws meeting on a steel bit at high torque; it doesn't take much wear or dust contamination to stop that working properly. The good news is that nine out of ten drill chuck problems are a cleaning job.
Open the chuck as wide as it will go and look inside. If you see grey dust on the jaws, that is brake dust from steel bits combined with masonry residue — it builds up over months and slowly stops the jaws closing fully on small bits. Compressed air or a stiff brush removes most of it; a drop of light penetrating oil on the threads, then opening and closing the chuck a dozen times, finishes the job. Wipe out the surplus or the next run of dust will stick to it.
If the jaws are visibly worn or chipped, no cleaning will save them. Replacement chucks fit onto a tapered or threaded spindle and come off with a sharp tap from a soft mallet — there is usually a left-hand thread screw inside the chuck that holds it down. Once off, the new chuck threads on hand-tight and seats with a single hard run-up against a piece of wood. The bigger picture on parts is on the tool parts hub.
Chuck problems also masquerade as bit problems. If only certain bits slip, the chuck is fine and the bits are at fault — round-shank bits with rolled flats wear smooth on hard work. A fresh set of drill and screwdriver bits usually restores grip in a way no chuck servicing will. For impact drivers, the issue is different: the 1/4” hex collet has a small ball that should snap into the groove on the bit. If your impact driver is dropping bits, the bits are non-impact-rated or the collet ball has lost its spring — a job for a replacement collet.
If a drill has stopped working entirely, the chuck is usually innocent. The first place to look is carbon brushes — the article on spotting worn brushes covers the symptoms.