A finite linear space S is an incident structure (P, L), where P is a set of v points and L is a set of b distinguished subsets of P called lines, such that any two points are incident with exactly one line. The linear space is said to be non-trivial if every line is incident with at least three points and there are at least two lines. If the sizes of all lines are equal, then we say that S is a regular linear space. An automorphism of S is a permutation of P which leaves L invariant. The full automorphism group of S is denoted by Aut(S) and any subgroup of Aut(S) is called an automorphism group of S. If an automorphism group G of S acts primitively on the set of points (resp. lines), then we say that G is point-primitive (resp. line-primitive). In this talk, I will introduce some classification results of finite regular linear spaces admitting point-primitive automorphism groups, especially the case when v=pq and 2pq, here p and q are primes.