Motions in biological tissues strongly influence their properties and are crucial for their functions. This is true starting from the scale of single molecules, all the way up to the scale of entire tissues. One of the key properties distinguishing motions in living systems from those in dead matter is activity: using chemical energy to generate self-propulsion. Effective theoretical, physics-based models are necessary both to interpret the rich new experimental observations in the field of biological motions, and to properly account for the inherent errors of the experimental methods. In this work we study models related to motion both on the level of tissues and individual molecules. One of our models is driven by the observation that many growing tissues form multicellular protrusions at their edges. It is not fully understood how these are initiated, therefore we propose a minimal continuum physical model to suggest a possible mechanism. We apply our model to a growing circular tumour. We employ our approach to understand how activity affects the tumour’s dynamics and the tendency to form “fingers” at its boundary. This approach rests on just four key biophysical parameters and we can estimate them based on experiments described in the literature. Our modelling of a tumour is experimentally well justified and analytically solvable in many systems. It is, to the best of our knowledge, the first analytical description of tumour interface dynamics incorporating the activity of the tumour bulk. We can explain the propensity of tissues to fingering instabilities, as conditioned by the magnitude of active traction and the growth kinetics. We are also able to derive predictions for the tumour size at the onset of metastasis, and predictions for the number of subsequent invasive fingers. Microscopy-based techniques are essential for observing biological motions at all aforementioned length scales. Brownian particle videotracking is one example of such a technique. In the second part of this thesis, we apply physics-based theory to understand inherent errors and limitations of this method. Using analytic solutions and simulations, we show the effects of errors in particle videotracking on recovering energy landscapes from the distributions of Brownian particles. We point out mechanisms that result in nontrivial systematic biases in the measurements.