Our world is becoming increasingly complex: nanoscale processes need to be understood for the next generation of materials; global financial markets need to be understood to be able to optimize and stabilize the world's economy; long time environmental forecasts need to be done to understand the impact of global warming. Many of the underlying questions in these fields involve abstract models and require accurate computational approximation. The models may not involve new, research mathematics, but are often beyond the expertise of application experts. Mathematicians have the skills to contribute to these questions. Several examples of successful collaboration of mathematicians in industrial problems will be outlined, including the speaker's work in a larger group working with Ballard Power Systems on simulation tools for Hydrogen fuel cells. Some of the challenges to this collaboration will be discussed, including resistance of industrial engineers to working with mathematicians, but also resistance by our own community to recognizing the value of this activity. Some additional remarks will be made on the employment opportunities for mathematicians working in Industry.