Modern armour does not really come in the form of a suit as such, but as with other eras, there are different pieces of protective garments that can be worn by soldiers, police officers, etc. As weapons have become stronger, the type of armour worn and the materials used to make it have had to evolve to ensure that the armour is effective.
Soldiers today will wear flak jackets that are made of a type of ballistic cloth such as Kevlar or spectra. Some include metal or ceramic plates. Soldiers in the US are using interceptor body armour, which has ‘Enhanced Small Arms Protective Inserts’ that are added to the areas around the chest, back and sides. Each of these plates has the ability to stop modern ammunition. British soldiers are using a type of body armour that is known as Osprey. This has the same effectiveness as the IOTV, which is the current body armour of choice of the US armed forces.
Other countries have adopted different makes of body armour, although generally most are made to the same standard. The Russians, for example, use the 6B43 and 6B45.