Gas giant planets at the widest separations can only be identified via high contrast imaging. Studying these planets allows us to understand the full architecture of exoplanetary systems, and to probe whether these objects are formed via a core accretion or a disk instability process. The high contrast imaging method is also unique in that stellar and planetary light are spatially separated, allowing detailed spectroscopic analysis of detected companions with a comparatively low observational cost. It has long been predicted that giant planets and circumstellar debris dust are linked, with planets such as β -Pictoris b and HD 106906 b residing in highly dusty systems. Of particular interest are those systems where the dust morphology is suggestive of the presence of planets: for example, in both the HR~8799 and HD~95086 systems one or more planets have been found in the gap between two belts of debris dust. Even the solar system is in this configuration, with the Asteroid and Kuiper belts enclosing the four gas and ice giants. In this work we carry out two surveys, where we search for planets using high contrast imaging. We survey both (a) 24 targets with the highest levels of circumstellar debris dust and (b) 20 targets with circumstellar disks, where infrared analysis suggests that the debris disk is carved into two distinct belts. For the second group of targets, the gap between the debris belts indicates the expected position of a giant planet within the system. Even further, we place constraints on the mass of the inferred planets in the system, based on the measured properties of the debris dust: the time taken to clear a gap in a debris disk is related to the mass of planets present. We can therefore calculate a minimum expected mass for planets in any particular system, based on the properties of the debris gap and the age of the system. These dynamical limits are complementary to observational limits we place on each system using high contrast imaging at the Very Large Telescope (VLT). These high contrast imaging surveys are carried out with the SPHERE instrument, a state-of-the-art high contrast imager, and we are typically sensitive to planets of a few Jupiter masses. These observational limits, along with the dynamical reasoning, allow tight constraints to be placed on the inferred planetary systems even when no planets are detected. While undertaking these surveys, we have made several new discoveries. Three of the debris disks were imaged in scattered light: two of these had never previously been resolved, while the third had been resolved with the Hubble Space Telescope at lower resolution and larger spatial scales. We detected two M-type companions to dusty targets, and a stellar binary with a moderate mass ratio. Finally, we identified a complex hierarchical quadruple stellar system, in which two of the four stars host debris disks based on their infrared excess.

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