Nowadays cryptography is applied in more and more applications. Most often asymmetric or hybrid systems are used, which are based on mathematical concepts. However, a promising family of quantum solutions tries to take over control. This article describes a technique of quantum key distribution called BB84. It gives an insight into quantum physics governing the proper operation of any system in quantum cryptography and then presents the detailed analysis of BB48 system. Its operation and security it provides are discussed. Next aspect that is covered is dedicated to practical considerations of quantum cryptography. All basic problems encountered while implementing BB84 or any other quantum system are explained.