Studies of structural and phase stabilities of metallic systems are of major interest both from the theoretical and experimental points of view. It has been established that in transition metals and alloys the number of d-electrons per atom Zd is responsible for the stability of a particular crystal structure. The variations of Zd with the atomic number or under high pressure may therefore lead to solid-solid structural transitions. Note that the situation may be quite complicated in a general case. It has been shown earlier that even at ambient pressure simple rigid band arguments may fail to predict electronic and structural properties of random alloys, particularly with increasing separation between the position of alloy components in the Periodic Table. High pressure adds one more degree of freedom into the problem. The main aim of the present work is to investigate theoretically the pressure induced phase transitions in several intermetallic systems. We will report on a detailed investigation of the combined effect of alloying and compression on the structural stability of random bcc and hcp alloys in the Mo-Re system. We will also discuss an interaction between iron and silicon at high pressure. The theory suggests that at low pressure, iron-silicon alloy is formed, but at high pressures corresponding, in particular, to Earth's core conditions, it dissociate into almost pure iron and the CsCl-structured (B2) FeSi compound. These predictions were confirmed experimentally, and the results are important for understanding of the properties of the Earth's core-mantle boundary.