  In this paper we develop several general methods for analysing
flag-transitive point-imprimitive $2$-designs, which give restrictions on both
the automorphisms and parameters of such designs. These constitute a tool-kit
for analysing these designs and their groups. We apply these methods to
complete the classification of flag-transitive, point-imprimitive
$2$-$(v,k,\lambda)$ designs with $\lambda$ at most $4$.
