There is today an increasing interest in environmental monitoring for a variety of specific applications, with great impact especially on natural resource management and preservation, economy, and people's life and health. Typical uses encompass, for example, Earth observation, meteorology, natural resource monitoring, agricultural and forest monitoring, pollution control, natural disaster observation and prediction, and critical infrastructure monitoring. While on one hand these systems play an important role in our society, on the other hand their adoption can raise a number of security and privacy concerns, representing a possible obstacle for the development of future environmental applications. In this paper, we analyze the security and privacy issues characterizing both the environmental monitoring infrastructures and the data collected and processed by them. We also provide an overview of possible countermeasures for diminishing the effects of these issues.