In a nutshell

MapProxy

MapProxy is an open source proxy for geospatial data. It speeds up mapping applications by pre-rendering and integrating maps from multiple sources and storing in a local cache. MapProxy is actively developed and supported by Omniscale. More information: http://mapproxy.org

Imposm

Imposm is an importer for OpenStreetMap data. It reads XML and PBF files and can import the data into PostgreSQL/PostGIS databases. It is designed to create databases that are optimized for rendering/WMS services. More informationen are available at: http://imposm.org