1 Introduction References 2 Theory of MW Emissions of Solar Flaring Loops 2.1 Observational Characteristics of Solar Microwave Emissions 2.1.1 Intensity, Polarization, and Spectrum of MW Emission 2.1.2 Radiation Transfer 2.1.3 Thermal and Nonthermal (NT) Emission 2.2 Gyrosynchrotron (GS) Emission 2.2.1 Emissivity and Self-absorption Coefficient 2.2.2 Formation of GS Spectrum 2.2.3 Influence of Magnetic Field Strength 2.2.4 Influence of Self-Absorption 2.2.5 Influence of High Plasma Density: Razin Effect 2.2.6 Razin Effect and Electron Power-Law Index 2.2.7 Plasma Density Increase on the Late Decay Phase.. 2.2.8 Influence of Plasma Inhomogeneity on GS Spectrum 2.3 Effects of Electron Pitch-Angle Anisotropy 2.3.1 Parameters of Numerical Simulation 2.3.2 Pitch-Angle Distributions of Sinu Type 2.3.3 Effect of Pitch-Angle Distribution Shape: Gaussian Loss-Cone 2.3.4 Effect of Pitch-Angle Distribution Shape: Beam-like Distribution 2.3.5 Discussion 2.4 Trapping and Transport Effects 2.4.1 Dependence on the Position of Acceleration/Injection Site 2.4.2 Spectral an Polarization Responses to Specific Electron Distributions 2.4.3 Diagnostic Potential 2.5 Effects of Other Parameters on GS Emission 2.5.1 Spectral Shape 2.5.2 Radio Flux Density 2.5.3 Spectral Index 2.5.4 Turnover Frequency 2.6 Numerical Codes for Fast GS Emission Calculations References 3 Observations and Explanations of MW Emissions in Solar Flaring Loops 3.1 Studies on Spatially Unresolvable Observations 3.1.1 Flattened Spectra in Solar Radio Bursts at Cm and Mm Bands and Dynamics of Energetic Electrons in Flaring Loops 3.1.2 Dynamics of Peak Frequency in Solar MW Bursts: Self-absorption and Razin Effect 3.1.3 Optically Thin Emission, Power-Law Distribution of Flares, and Occurrence Rate of Flares 3.2 Spatial Distribution of Microwave Brightness 3.2.1 Nonthermal MW Source at the Top of Extended Flaring Loops 3.2.2 Time Delays Between MW Emissions from Different Parts of Flaring Loop 3.2.3 Time Delays of MW Emissions at Different Frequencies 3.2.4 Redistribution of MW Brightness in Flaring Loops 3.2.5 Comparison of Observations and Model Predictions 3.2.6 Spatial Distribution of Energetic Electrons in Flaring Loops 3.2.7 Dynamics of Electron Spatial Distribution 3.2.8 Constraints on Particle Acceleration, Projection, and Motion 3.3 Statistical Studies on MW Brightness Distributions 3.3.1 Data Selection 3.3.2 Comparison of MW Brightness in LT and FPs 3.3.3 Relation of MW Brightness and Other Parameters 3.3.4 Asymmetry of MW Brightness in Flaring Loop FPs 3.4 Spectral Properties of MW Emissions 3.4.1 Distribution of Spectral Slopes Along Flaring Loops 3.4.2 Statistics of Optically Thin Spectral Indices of MW Emissions in LT and FPs 3.4.3 Hard-Soft-Hard (HSH)--a New Pattern of MW Spectral Evolution 3.4.4 Dependence of Spectral Evolution on Frequencies 3.4.5 Evolution of MW Spectra in Different Parts of Flaring Loops 3.5 Distribution and Evolution of Radio Polarization 3.5.1 Comparison of Polarization of MW Emissions in LT and FPs 3.5.2 Relation of Polarization and Other Parameters in LT and FPs 3.5.3 Relation of Polarization and Magnetic Field in LT and FPs 3.5.4 Time Variation of Polarization in LT and FPs 3.5.5 Linear Mode Coupling and Reversal of Polarization 3.5.6 Determination of Intrinsic Mode 3.5.7 Modeling the MW Polarization Distribution Along Flaring Loops References Theory of X-Ray Emissions in Solar Flaring Loops 4.1 Thick-Target and Thin-Target Models 4.1.1 Overview 4.1.2 Thin-Target Model 4.1.3 Thick-Target Model 4.1.4 Relation of Two Models 4.1.5 Effect of Low-Energy Cutoff on Spectral Indices of Electrons and Photons 4.2 Propagation of Electrons and Its Effect on X-Ray Emission 4.2.1 Overview 4.2.2 Magnetic Mirror and Loss-Cone Distribution 4.2.3 Formation of Loss-Cone Distribution 4.3 Spatial Distribution of X-Ray and 7-Ray Brightness 4.3.1 Numerical Simulations of Spatial Distribution of Energetic Electrons in Flaring Loops 4.3.2 Simulated Results of Spatial Distribution of X-Rays and y-Rays 4.3.3 Conclusions 4.4 Spatial Distribution of X-Ray Directivity and Polarization 4.4.1 Modeling 4.4.2 Directivity at Different Positions in Flaring Loops 4.4.3 Polarization at Different Positions in Flaring Loops 4.4.4 Conclusions References 5 Observations and Explanations of X-Ray Emissions in Flaring Loops 5.1 Overview 5.2 Distribution of Hard X-Ray (HXR) Brightness: Loop Top and Feet 5.3 Spectral Index of HXR Emissions: Loop Top and Feet 5.4 A New Pattern of HXR Spectral Evolution 5.5 Evolution of HXR Spectra in Dependence of Energies 5.6 Evolution of HXR Spectra in Dependence of Locations 5.7 Asymmetry of HXR Brightness in Flaring Loop Feet References 6 Diagnostics of Flaring Loop Parameters 6.1 Overview 6.2 Diagnosis of Coronal Magnetic Field and Non-thermal Electron Density 6.2.1 Diagnosis Method 6.2.2 Sudden Change of Transverse Coronal Magnetic Component Around Magnetic Neutral Line 6.2.3 Attenuation of Coronal Magnetic Field in Solar MW Bursts 6.2.4 Evolution of Turnover Frequency and Magnetic field with Flattened Optically Thin Spectra 6.2.5 Theoretical Scaling Laws of Coronal Magnetic Field and Electron Power-Law Index in Corona 6.2.6 Comparison of Radio Diagnosis with Extrapolation of Solar Photospheric Magnetogram 6.2.7 Summary and Prospective 6.3 Diagnosis of Low-Energy Cutoff and Spectral Index of NT Electrons 6.3.1 Meaning and Debate of Low-Energy Cutoff 6.3.2 Cross Point of Spectral Lines at Different Times 6.3.3 Relation of Low-Energy Cutoff and Ratio of Radiation Intensities or Spectral Index 6.3.4 Joint Effect of Low-Energy Cutoff and Compton Scattering on Flattened Spectra at Lower Energies 6.3.5 Low-Energy Cutoff and Spectral Index of MW and HXR with Two Methods 6.3.6 Low-Energy Cutoff and Spectral Index of MW and HXR with Strict Methods 6.3.7 Discussions and Conclusions 6.4 Diagnosis of Pitch-Angle of NT Electrons 6.4.1 Overview 6.4.2 Diagnosis of Mirror Ratio of Coronal Loops 6.4.3 Diagnosis of Initial Pitch-Angle 6.5 Evidence for Dynamic Evolution of Energetic Electron Spectrum 6.5.1 Overview 6.5.2 Theoretical Prediction of MW and HXR Spectral Evolution 6.5.3 Observational Data 6.5.4 Theoretical Simulation of Electron Spectral Evolution in MW Sources 6.5.5 Conclusions 6.6 Diagnosis of Acceleration Site and Pitch-Angle Distribution of Accelerated Electrons 6.6.1 Overview 6.6.2 Observations 6.6.3 Evolution of Brightness Distribution 6.6.4 Discussions 6.6.5 Conclusions 6.7 Inversion of NT Electron Spectral Index 6.7.1 Overview 6.7.2 Comparison of NT Spectral Indices of MW and X-Ray Emissions in Solar Flares 6.7.3 Summary 6.8 Radio Diagnostics of the Solar Flaring Loop Parameters 6.8.1 Method for Recovering Flaring Loop Parameters 6.8.2 Determination of Model Radio Source Parameters 6.8.3 Recovering Physical Parameters of Solar Flaring Loops 6.8.4 Conclusions References 7 Global Behaviors for Dynamics of Flaring Loops 7.1 Global Behaviors Revealed by Observations at Multi-wavebands 7.1.1 Contraction of Flaring Loops prior to Their Expansion 7.1.2 The Relaxation of Sheared Magnetic Field 7.1.3 Possible Impact on the Lower Atmosphere 7.1.4 Sigmoid Magnetic Ropes 7.2 Failed Eruption of Filaments 7.3 Dynamics of MW and HXR Flaring Loop System 7.3.1 Introduction 7.3.2 Observations 7.3.3 Morphological Feature of AR10798 at H-Alpha and EUV in Pre-flare Phase 7.3.4 Radio, Optical, and X-Ray Images of Flaring Loops 7.3.5 Time Profiles 7.3.6 Evolution of Spatial Characteristic Parameters 7.3.7 Trajectories of Flaring Loop Top and Feet 7.3.8 Discussions 7.3.9 Conclusions 7.4 Quasi-periodic Pulsations (QPPs) in Microwave Band 7.4.1 Types of QPPs in Microwave Band 7.4.2 Theoretical Explanations of QPPs 7.4.3 Relation of Repetition Rate and Burst Flux in QPPs 7.5 Motion of X-Ray Sources Along Flaring Loops 7.5.1 Overview 7.5.2 Motion of X-Ray Sources Along Flaring Loops 7.5.3 Summary 7.6 Interaction of Flaring Loops 7.6.1 Typical Examples of Loop Interaction 7.6.2 Statistical Evidence of Loop Interaction 7.6.3 Conclusions 7.7 Numerical Models and Observations of Chromosphere Evaporation 7.7.1 Introduction 7.7.2 Numerical Models 7.7.3 Observations of Chromospheric Evaporation 7.7.4 X-Ray and Radio Imaging Observations 7.7.5 Summary References Appendix: Color Figures Index