Abstract This year we celebrate the tenth anniversary of the achievement of Bose-Einstein condensation (BEC) in cold alkali atomic gases. Interestingly, current efforts in this field are directed towards the experimental realization of strongly correlated systems with no condensate. In this seminar, after a brief introduction, we shall describe two examples of this ongoing effort to "break up the condensate". The first example deals with optical lattices and their use to produce low-dimensional quantum gases. In particular, we will focus on some aspects of the recent theoretical and experimental activity seeking to produce one-dimensional strongly correlated quantum gases with bosonic atoms. In the second part of the seminar, we will describe some interesting quantum phenomena that occurs in the limit where a Bose gas is rotated at increasingly rapid frequencies.