Abstract The main feature of a basis {fk} ∞ k=1 in a Hilbert space H is that every f ∈ H can be represented by an infinite linear combination of the elements fk in the basis: f = X∞ k=1 ck(f)fk. (1) The coefficients ck(f) are unique. The key question in understanding the frames theory can be simply stated as follows: is the uniqueness of coefficients ck(f) really needed? In this talk, after recalling some basic facts about bases, we introduce the concept of frames. A frame is also a sequence of elements {fk} ∞ k=1 in H, such that each element f ∈ H can be represented as in (1). However, the frame elements are not necessarily linearly independent and the corresponding coefficients are not necessarily unique. Thus a frame might not be a basis. Related to the frames concept there is the concept of waveform dictionary. The waveform dictionary is a large set that contains more information than required. The waveform dictionary contains the wavelet dictionary (system) and the Gabor system providing a flexible collection of functions with desirable properties from both. The aim of this talk is just to review the arguments for generalizing the basis concept to frames and waveform dictionaries.