Planetary systems form in disks of gas and dust surrounding newborn stars. The young circumstellar environment is characterized by frequent collisions between rocky bodies, leading to a continuous production of small dust grains. Such collisional processing persists in leftover debris disks or belts akin to the Solar System's asteroid and Kuiper belts, during the star's entire main-sequence lifetime. This thesis presents observations of thermal emission from cold dust in extended debris disks, in addition to spatially resolved observations of dust scattered light and gas emission in nearby debris disk systems. A total of 30 debris disk candidates identified from infrared excess were observed at submillimeter (submm) wavelengths with the Atacama Pathfinder EXperiment (APEX) telescope in search for dust at radial distances corresponding to the Kuiper belt or beyond. Two observing campaigns with the PolCor instrument at the Nordic Optical Telescope (NOT), performing optical polarimetric coronagraphy to resolve scattered light from nearby disks were also carried out. The edge-on debris disk surrounding the star β Pictoris was explored using integral-field spectroscopy with the Very Large Telescope (VLT) in an attempt to map the spatial distribution of previously detected gas. The APEX observations detected 14 exo-Kuiper belts, out of which 7 were new discoveries in the submm region. Modeling of the spectral energy distribution from available photometry and detected submm fluxes allowed us to study the dependence of the fractional dust luminosity and characteristic radial dust distance on stellar spectral type and age. The results indicate a decrease in fractional dust luminosity as t^-α, where t is the age of the system and α = 0.8–2.0. From the VLT data we retrieved the first complete image of Ca II and Fe I emission in the disk of β Pictoris. Subsequent modeling demonstrated that the anomalous vertical structure of the observed Ca II emission can be explained by an optically thick disk midplane.