Lead paint
Lead paint is paint containing lead, which was used until the 1970s as a white pigment. White pigment does not add color, but serves the very important function of increasing opacity and making the paint resistant to UV radiation. For centuries, the primary white pigment in paints was lead white (basic lead carbonate, 2PbCO3·Pb(OH)2), one of the oldest pigments known. One problem with lead is that it is extremely toxic, and as lead white ages it turns to lead acetate, which is sweet to taste. This is why children had the tendency to lick or chew on woodwork painted with lead white paint.
One practical way to protect children from lead based paint and lead poisoning is to simply repaint with any modern paint and to repaint any areas where the paint peels or chips in a timely fashion. Children will be unlikely to consume any lead paint because the newly painted surface will not taste sweet. There are many laws regarding lead-based paint remediation, so you may be required to do more than repainting. In preparing the surface for painting, be aware that sanding may create undesirable lead dust; it is preferable to use a liquid sander/degreaser.
Lead test kits are used to test for the presence of lead, but an informed guess can be made if the date of construction of a home is known. Lead white was widely used in paints in the USA until about 1960, when the danger of lead white in paints became known. It was rapidly replaced by paint manufacturers and by the time national legislation came into effect in 1978 outlawing its use in the USA, lead was uncommon as a pigment. Homes older than 1960 almost certainly contain lead paint, homes built between 1960 and 1965 are likely to contain lead paint, whilst those built between 1966 and 1978 are not likely to. Homes built after 1978 probably do not contain lead paint.
Paint manufacturers replaced lead white with a less toxic substitute, titanium white or Titanium dioxide which was first used in paints in the 19th century. Titanium Dioxide is safe to use as a food colouring. The titanium white used in most paints today is often coated with silicon or aluminum oxides for better durability.