Web processes are the next generation workflows created using Web services. This paper addresses research issues in creating a framework for configuring and executing dynamic Web processes. The configuration module uses Semantic Web service discovery, integer linear programming and logic based constraint satisfaction to configure the process, based on quantitative and non-quantitative process constraints. Semantic representation of Web services and process constraints are used to achieve dynamic configuration. An execution environment is presented, which can handle heterogeneities at the protocol and data level by using proxies with data and protocol mediation capabilities. In cases of Web service failures, we present an approach to reconfigure the process at run-time, without violating the process constraints. Empirical testing of the execution environment is performed to compare deployment-time and run-time binding.