The talk is devoted to the development of the metric, dimensional and probabilistic theories of ML-expansions which contain as special cases generalized Lüroth expansions, alternating Lüroth expansions, $I$-$Q_\infty$-expansions and many others.

Fractal properties of spectra of random variables with independent identically distributed ML-symbols are studied in details and new fractal phenomena will be presented.

We also discuss fine fractal properties of the corresponding singularly continuous probability measures and derive exact formulae for the determination of the Hausdorff dimension of minimal (in dimensional meaning) supports of the measures.