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A few years ago, it was proposed to use the simultaneous quantification of unspliced and spliced messenger RNA (mRNA) to add a temporal dimension to high-throughput snapshots of single cell RNA sequencing data. This concept can yield additional insight into the transcriptional dynamics of the biological systems under study. However, current methods for inferring cell state velocities from such data (known as RNA velocities) are afflicted by several theoretical and computational problems, hindering realistic and reliable velocity estimation. We discuss these issues and propose new solutions for addressing some of the current challenges in consistency of data processing, velocity inference and visualisation. We translate our computational conclusion in two velocity analysis tools: one detailed method κ-velo and one heuristic method eco-velo, each of which uses a different set of assumptions about the data. Author summary: Single cell transcriptomics has been used to study dynamical biological processes such as cell differentiation or disease progression. An ideal study of these systems would track individual cells in time but this is not directly feasible since cells are destroyed as part of the sequencing protocol. Because of asynchronous progression of cells, single cell snapshot datasets often capture cells at different stages of progression. The challenge is to infer both the overall direction of progression (pseudotime) as well as single cell specific variations in the progression. Computational methods development for inference of the overall direction are well advanced but attempts to address the single cell level variations of the dynamics are newer. Simultaneous measurement of abundances of new (unspliced) and older (spliced) mRNA in the same single cell adds a temporal dimension to the data which can be used to infer the time derivative of single cells progression through the dynamical process. State-of-the-art methods for inference of cell state velocities from RNA-seq data (also known as RNA velocity) have multiple unaddressed issues. In this manuscript, we discuss these issues and propose new solutions. In previous works, agreement of RNA velocity estimations with pseudotime has been used as validation. We show that this in itself is not proof that the method works reliably and the overall direction of progression has to be distinguished from individual cells' behaviour. We propose two new methods (one detailed and one cost efficient heuristic) for estimation and visualisation of RNA velocities and show that our methods faithfully capture the single-cell variances and overall trend on simulation. We further apply the methods to different datasets and show how the method can help us gain biological insight from real data. [ABSTRACT FROM AUTHOR]