| It has been proved by experiment, that quantum states of cavity field can exhibit three non-classical features, i.e. photon antibunching effect, sub-Poissonian statistics distribution, and squeezed states. In quantum states which have squeezing effect, one quadrature phase may have reduced quantum fluctuations compared with what the relative quadrature phase have in coherent states, this make it have different applications in optical communication systems, and so on. Therefore, squeezed states of the radiation field is still a central topic in quantum optics. On the one hand, experiments have been performed in which squeezed light can be generated; on the other, people always make a search for methods of generating highly squeezed states intensely.This review aims to present a number of schemes for generating quantum states of the radiation field, and to discuss the squeezing property as well as other nonclassical properties of some quantum states. This review is organized as follow: 1. Generating a superposition of squeezed states via Raman interaction of degenerate A-type three-level atoms with single-mode cavity fields. The problem of control of squeezing angle (squeezing direction) in optical fields of single-mode squeezed coherent states is discussed in detail. 2. Preparing entangled states of single-mode cavity and a moving-mirror, Schrodinger cat states in the cavity with a moving-mirror by using the interaction of single-mode cavity and moving-mirror. Generating a superposition of Fock states of the cavity field by measuring the position coordinate of the mirror in the cavity. We then discuss the squeezing and coherence properties of the cavity. By using numerical calculation, we find that the cavity has some nonclassical properties. It presents squeezing effect andantibunching effect. 3. A discussion is made about the squeezing properties of several superpositions, the vacuum state with coherent state or odd- and even-coherent-state. It is found that the vacuum state has important value in squeezing. |