The interest for reducing the energy consumption in society has increased during the last decades due to an increased environmental awareness. One way to decrease the energy losses in the building sector is to improve the thermal insulation of building envelopes and installations and thereby decrease the heat losses. This thesis analyzes two types of novel insulation with low thermal conductivity; aerogel blankets and vacuum insulation panels. The thesis aims to investigate the possible benefits from using these novel insulations, but also to evaluate new considerations related to the high insulation performance. The insulations have been tested in two applications: 1.A wooden stud wall with aerogel blankets as insulation2.Hybrid insulated district heating pipes where aerogel blankets or vacuum insulation panels have been wrapped around the carrier pipe and polyurethane have been used to fill the rest of the casing pipe.Thermal properties and moisture properties have been measured in laboratory by guarded heat flow meter, guarded hot pipe, transient plane source and wet cup method. District heating pipes with vacuum insulation panels have also been measured in field. The measured properties have been used in numerical simulations to evaluate the heat losses and the risk of moisture related damages for both applications.The studies show promising results for aerogel blanket insulated walls where the wall thickness was reduced by 40 percent compared to a conventional Swedish wall. However, the effect on the moisture conditions from the thermal bridges through the studs has to be considered in order to avoid damages. For district heating pipes, the vacuum insulation panels showed the most promising results with a decrease in the heat losses by 15 to 25 percent depending on the dimensions of the pipe and the thickness of the vacuum insulation panels. In hybrid insulation double pipes with vacuum insulation, the position of the thermal bridges at the edges of the panel has a large impact on the total heat losses. The thesis also examines some challenges when measuring the properties of the novel insulation. The thermal conductivity of aerogel blankets improves with an increased compression of the samples. The properties of the curved vacuum insulation panels used in the district heating pipes are difficult to measure since there is an impact from the thermal bridges along the edges, which might be influenced by surrounding materials.