Positive polarized muons (μ⁺) act as non-destructive, non-invasive, and microscopic probes for local investigations. Over the years they have provided unique information about magnetic, superconducting and other electronic properties of bulk matter. A novel extension of the μSR technique is given by the availability of μ⁺ with 100% spin polarization, and whose energy can be continuously varied from 0.5 to 30 keV. This allows depth-dependent μSR-studies of thin films, near-surface regions and multilayered structures in the range from ∼1 to ∼300 nm. After a brief introduction of the present status of this technique, some experiments are overviewed including depth-dependent studies of thin films and heterostructures of various magnetic and superconducting materials, ranging from cuprates through spin glasses to structures and compounds relevant to spintronics applications.