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The aim of the article is to provide a clear and thorough conceptual analysis of the main candidates for a definition of climate and climate change. Five desiderata on a definition of climate are presented: it should be empirically applicable; it should correctly classify different climates; it should not depend on our knowledge; it should be applicable to the past, present, and future; and it should be mathematically well-defined. Then five definitions are discussed: climate as distribution over time for constant external conditions; climate as distribution over time when the external conditions vary as in reality; climate as distribution over time relative to regimes of varying external conditions; climate as the ensemble distribution for constant external conditions; and climate as the ensemble distribution when the external conditions vary as in reality. The third definition is novel and is introduced as a response to problems with existing definitions. The conclusion is that most definitions encounter serious problems and that the third definition is most promising. 1 Introduction 2 Climate Variables and a Simple Climate Model 3 Desiderata on a Definition of Climate 4 Climate as Distribution over Time 4.1 Definition 1: Distribution over time for constant external conditions 4.2 Definition 2: Distribution over time when the external conditions vary as in reality 4.3 Definition 3: Distribution over time for regimes of varying external conditions 4.4 Infinite versions 5 Climate as Ensemble Distribution 5.1 Definition 4: Ensemble distribution for constant external conditions 5.2 Definition 5: Ensemble distribution when the external conditions vary as in reality 5.3 Infinite versions 6 Conclusion Appendix 1 Introduction 2 Climate Variables and a Simple Climate Model 3 Desiderata on a Definition of Climate 4 Climate as Distribution over Time 4.1 Definition 1: Distribution over time for constant external conditions 4.2 Definition 2: Distribution over time when the external conditions vary as in reality 4.3 Definition 3: Distribution over time for regimes of varying external conditions 4.4 Infinite versions 4.1 Definition 1: Distribution over time for constant external conditions 4.2 Definition 2: Distribution over time when the external conditions vary as in reality 4.3 Definition 3: Distribution over time for regimes of varying external conditions 4.4 Infinite versions 5 Climate as Ensemble Distribution 5.1 Definition 4: Ensemble distribution for constant external conditions 5.2 Definition 5: Ensemble distribution when the external conditions vary as in reality 5.3 Infinite versions 5.1 Definition 4: Ensemble distribution for constant external conditions 5.2 Definition 5: Ensemble distribution when the external conditions vary as in reality 5.3 Infinite versions 6 Conclusion Appendix