  The perturbative QCD predictions concerning deep inelastic scattering at low
$x$ are summarized. The theoretical framework based on the leading log $1/x$
resummation and $k_t$ factorization theorem is described and some recent
developments concerning the BFKL equation and its generalization are discussed.
The QCD expectations concerning the small $x$ behaviour of the spin dependent
structure function $g_1(x,Q^2)$ are briefly summarized and the importance of
the double logarithmic terms which sum contributions containing the leading
powers of $\alpha_s ln^2(1/x)$ is emphasised. The role of studying final states
in deep inelastic scattering for revealing the details of the underlying
dynamics at low $x$ is pointed out and some dedicated measurements, like deep
inelastic scattering accompanied by an energetic jet, the measurement of the
transverse energy flow etc., are briefly discussed.
