We describe the limits of current practice in analysing data while preserving privacy; explain emerging privacy-preserving computation techniques; and outline key challenges to bringing these technologies into mainstream use. For each technology addressed, we technical overview; examples of applied uses;An explanation of modelling adversaries and security arguments that typically apply;An overview of the costs of using the technology;An explanation of availability of the technology;and a Wardley map that illustrates the technology readiness and suggested development focus for the technology.